Course Structure of Undergraduate Mathematics Programme

Mathematics undergraduate programme has been designed including topics of current interest and applications. Once a student undergoes this course successfully he will be well equipped to face the challenges of life. The programme of study includes courses for improving communication skills, strengthening basic science and computational mathematics background and acquainting the student with the socio-economic & historical background of Bangladesh. With this background it should not also be a problem to find a suitable and satisfying job in both public and private sectors, various universities, financial institutions and software & R/D organizations in the country. The total credit requirement for the degree of Bachelor of Science in Mathematics is 127. Out of these 21 credits are for general education. Nineteen major area compulsory courses account for 57 credits. The students are required to complete 2 courses (4 credits) of Mathematics Lab and write a dissertation on a suitable project/thesis topic. The project/thesis work spread over the last two semesters will have a total of 3 credits. The students will be required to complete 15 credits choosing from several elective courses in their major field and 27 credits from outside their major specialization. The students may also be required to take noncredit remedial courses in English.

Courses for Bachelor of Science in Mathematics

The graduation programme for Mathematics will contain the courses as appended below . However, the courses listed below may change as the need arises in future.

a. General Education (21 credits)

1 BIO 101 Introduction to Biology
2 CSE 110 Programming Language I
3 DEV 101 Bangladesh Studies
4 ENG 091 Foundation Course (Non-credit)
5 ENG 101 English Fundamentals *
6 ENG 102 Composition I *
7 HUM 103 Ethics and Culture
8 PHY 111 Principles of Physics I

b. Departmental Core Courses: (57 credits)

1 MAT 111 Principles of Mathematics
2 MAT 121 Basic Algebra
3 MAT 122 Analytic and Vector Geometry
4 MAT 123 Calculus I
5 MAT 124 Scientific Programming
6 MAT 211 Calculus II
7 MAT 212 Linear Algebra
8 MAT 221 Real Analysis I
9 MAT 222 Differential Equations I
10 MAT 223 Numerical Analysis I
11 MAT 311 Abstract Algebra
12 MAT 312 Numerical Analysis II
13 MAT 314 Complex Analysis
14 MAT 321 Real Analysis II
15 MAT 322 Differential Equations II
16 MAT 323 Dynamical Systems
17 MAT 324 Graph Theory
18 MAT 325 Mathematical Methods
19 STA 201 Elements of Statistics and Probability

c. Elective Courses: (15 credits)

1 CSE 220 Data Structures
2 CSE 221 Algorithms
3 MAT 313 Differential Geometry
4 MAT 316 Operations Research I
5 MAT 326 Hydrodynamics
6 MAT 411 Topology
7 MAT 415 Finite Element Methods
8 MAT 416 Tensor Calculus
9 MAT 421 Fluid Mechanics
10 MAT 422 Theory of Numbers
11 MAT 423 Mathematical Modeling
12 MAT 424 Operations Research II
13 MAT 425 Advanced Numerical Methods
14 PHY 112 Principles of Physics II
15 PHY 204 Classical Mechanics and Special Theory of Relativity
16 PHY 205 Statistical Mechanics
17 PHY 303 Quantum Mechanics I
18 PHY 413 General Theory of Relativity
19 STA 301 Modern Probability Theory & Stochastic Processes

d. Lab: (4 credits)

**1 MAT 250 Mathematics Lab I
**2 MAT 350 Mathematics Lab II

e. Project / Thesis: (3 credits)

1 MAT 400 Project / Thesis

f. Courses Outside Major Specialization: (27 credits)

1 ANT 101 Introduction to Anthropology
**2 ARC 292* Painting
**3 ARC 293* Music Appreciation
4 CHE 101 Introduction to Chemistry
5 ECO 103 Principles of Economics
6 ENV 101 Introduction to Environmental Science
7 HUM 101 World Civilization and Culture
8 HUM 102 Introduction to Philosophy
9 HUM 111 History of Science
10 MAT 315 History of Mathematics
11 MGT 211 Principles of Management
12 PHY 312 Physics for Development
13 POL 103 Introduction to Political Science
14 POL 245 Women, Power & Politics
15 PSY 101 Introduction to Psychology
16 SOC 101 Introduction to Sociology
17 SOC 401 Gender and Development

or any other BRAC University courses outside major specialization.
* Other courses in English may substitute these courses depending on the level of the student's proficiency in English. ** 2 Credit Courses

Academic System & Evaluation Method

a. Academic Standards

In keeping with the mission and goals in mind, every effort will be made to ensure high academic standards by implementing well-designed curricula, carefully selecting high quality students and faculty, utilising modern and effective instructional methods and aides, and by continuously monitoring and rigorously evaluating all the pertinent activities and systems. A special feature of teaching will be the lab/workshop sessions designed to assist students in learning application of the concepts and theories.

b. Courses and Credit Requirements

The Bachelor of Science programme in Mathematics will follow the model of higher education consisting of semesters, courses, credit hours, continuous evaluation and letter grading as in all other courses of BRAC University. The undergraduate curriculum consists of general education courses, major courses, elective courses and non-major area courses.

c. Examination, Evaluation and Grading

The grading process will undoubtedly be transparent. The performance of the students is evaluated throughout the semester through class tests, quizzes, assignments, and midterm exams. End of semester evaluation includes final examinations, term papers, project reports
etc. Numerical scores earned by a student in tests, examinations, assignments etc. are cumulated and converted to letter grades.

d. Distribution of Marks & GPA Computation

The distribution of marks for the performance evaluation is as follows:

i. Theory Courses

Section Marks %
1. Quizzes/ Class Tests/ Assignments/ Participation/ Attendance 30
2. Mid Term Examination 20
3. Final Examination (comprehensive), Projects 50
Total Marks 100

ii. Lab Courses

Section Marks%
1. Reports/ Class Tests/ Participation / Viva-Voce 30
2. Lab Experiments 30
3. Final Examination 40
Total Marks 100

iii. Project / Thesis

Project / Thesis work will be spread over the last two semesters of study. The mark distribution for the Project / Thesis will be as follows:

Section Marks %
1. Viva-Voce 15
2. Thesis / Project Work 45
3. Defence 40
Total Marks 100

Class attendance is compulsory for every student. 5% of total marks in every course is allocated for attendance in classes including tutorials and labs. The basis for awarding marks for attendance is as follows:

Attendance Marks
90% and above 5
85% to less than 90% 4
80% to less than 85% 3
75% to less than 80% 2
70% to less than 75% 1
Less than 70% 0

If a student does not attend a minimum of 70% of the total classes including tutorials and labs, s/he will not be allowed to take the final exam.

Marks earned by the students in Class Tests, Quizzes, Assignments, Participation, Attendance, Midterm Exam , Final Exam, Projects, Term Papers etc are to be cumulated and the total is to be graded as per the existing BRAC University rules and regulations :

GPA Computation

The Grade Point Average (GPA) is computed in the following manner:

            Sum of (Grade points Credits)

GPA =  ------------------------

            Sum of Credits Attempted

Course Contents

a. Theoretical Courses:

ANT 101 Introduction to Anthropology 3 credits

Humans in nature, human evolution, history of culture, rise of early civilizations in the old and new world, organizations of pre-industrial society environment, resources and their distribution; gender, kinship and descent, religion, economics, politics, survival of indigenous groups, forms of culture and society among contemporary peoples, Comparative study of traditional and changing Third World societies, impact of modern world on traditional societies, power and social order; custom and law, conflict and change, Cultural and ethnic diversity.

Recommended Books:

1. Cultural Anthropology, a Global Perspective: R Scupin
2. Anthropology: The Exploration of Human Diversity: Conrad P Kottak
3. Anthropology: C Ember and M Ember
4. Cultural Anthropology: W A Haviland
5. Anthropology - Social and Cultural: Kedar Nath, Ram Nath
6. An Introduction to Anthropology: Victor Barnouw.

ARC 292 Painting 2 credits

Painting as a form of artistic and architectural expression. Introduction to various media in painting. Still life sketches and painting. Study of forms in painting. Landscapes and cityscapes. Colour pencils, crayons, pastels and watercolour. Mixed media. Computers in painting.

ARC 293 Music Appreciation 2 credits

Musical form. Ingredients of music: sound and time. Indian and Western music: melody and harmony. Foundations of sub-continental music: raga system. Presentation of vocal and instrumental music. Modern Bengali music and works of major composers and demonstrations. Western classical music and works of major composers. Music and its rhythm, composition etc.

BI0 101 Introduction to Biology 3 credits

An introduction to the cellular aspects of modern biology including the chemical basis of life, cell theory, energetics, genetics, development, physiology, behaviour, homeostasis and diversity, and evolution and ecology. This course will explain the development of cell 11 structure and function as a consequence of evolutionary process, and stress the dynamic property of living systems.

Recommended Books:

1. Biology: P.H. Raven and G.B. Johnson
2. Biological Science: G. W. Stout and D. J. Taylor
3. Advanced Biology: J. Simpkins and J. J. Williams
4. Biology: A Fundamental Approach: M. B. Roberts

CHE 101 Introduction to Chemistry 3 credits

The course is designed to give an understanding of basics in chemistry. Topics include nature of atoms and molecules; valence and periodic tables, chemical bonds, aliphatic and aromatic hydrocarbons, optical isomerism, chemical reactions.

Recommended Books:

1. Introduction to Modern Inorganic Chemistry: S. Z. Haider
2. Physical Chemistry: Haque & Nawab
3. Organic Chemistry: R. T. Morrison & R. N. Boyd
4. General Chemistry: Raymond Chang

CSE 110 Programming Language I 3 credits

An introduction to the foundations of computation and purpose of mechanised computation, techniques of problem analysis and the development of algorithms and programs, principles of structured programming and corresponding algorithm design, Topics will include data structures, abstraction, recursion, iteration as well as the design and analysis of basic algorithms, (language C is primarily used), introduction to digital computers and programming algorithms and flow chart construction, information representation in digital computers, writing, debugging and running programs (including file handling) on various digital computers using C. The course includes a compulsory 3 hours laboratory work each week.

Recommended Books:

1. Working with C: Y Kanetkar
2. Schaums Outline of Theory and Problems of Programming With C: Byron S. Gottfried

CSE 220 Data Structures 3 credits

Introduction to widely used and effective methods of data organization, focusing on data structures, their algorithms and the performance of these algorithms. Concepts and examples, elementary data objects, elementary data structures, arrays, lists, stacks, queues, graphs, trees, compound structures, data abstraction and primitive operations on these structures. Memory management; sorting and searching; hash techniques. Introduction to the fundamental algorithms and data structures: recursion, backtrack search, lists, stacks, queues, trees, operation on sets, priority queues, graph dictionary. Introduction to the analysis of algorithms to process the basic structures. A brief introduction to database systems and the analysis of data structure performance and use in these systems.

Recommended books:

1. Data Structure and Program Design: Robert L Kruse; PrenticeHall.
2. Data Structures, Algorithms, and Software Principles in C: Thomas A Standish; PrenticeHall.
3. Data Structures and Algorithm Analysis in C: Mark Allen Weiss; Addison Wesley; Longman Inc.
4. Data Structure: Edward M Reingold, Wilfred J Hansen; CBS Publishers & Distributors.
5. Data Structures in C++: Using the Standard Template Library; Timothy Budd; Addison Wesley Longman Inc.

CSE 221 Algorithms 3 credits

The study of efficient algorithms and effective algorithm design techniques. Techniques for
analysis of algorithms, Methods for the design of efficient algorithms: Divide and Conquer paradigm, Greedy method, Dynamic programming, Backtracking, Basic search and traversal techniques, Graph algorithms, Elementary parallel algorithms, Algebraic simplification and transformations, Lower bound theory, NP-hard and NP-complete problems. Techniques for the design and analysis of efficient algorithms, Emphasising methods useful in practice. Sorting; Data structures for sets: Heaps, Hashing; Graph algorithms: Shortest paths, Depth-first search, Network flow, Computational geometry; Integer arithmetic: gcd, primality; polynomial and matrix calculations; amortised analysis; Performance bounds, asymptotic and analysis, worst case and average case behaviour, correctness and complexity. Particular classes of algorithms such as sorting and searching are studied in detail. The course includes a compulsory 3 hour laboratory work alternate week.

Recommended books:

1. Introduction to Algorithms: Thomas H Cormen, Charles E Leiserson, Ronald L Rivest, Clifford Stein; McGrawHill.
2. Fundamentals of Computer Algorithms: Ellis Horowitz, Sartaj Sahni; Galgotia Publications.
3. Fundamental Algorithms: The Art of Computer Programming. vol. 1; Donald E Knuth.
4. Seminumerical Algorithms: The Art of Computer Programming. vol. 2; Donald E Knuth.
5. Sorting and Searching: The Art of Computer Programming. vol. 3; Donald E Knuth.
6. Data Structures and Algorithm Analysis in C: Mark Allen Weiss; Addison Wesley Longman Inc.

DEV 101 Bangladesh Studies 3 credits

Socio-economic profile of Bangladesh, agriculture, industry, service sector, demographic patterns, social aid and physical infrastructures. Social stratification and power, power structures, government and NGO activities in socio-economic development, national issues and policies and changing society of Bangladesh.

Recommended Books:

1. Bangladesh, National Cultures and Heritage , An Introductory Reader: A.F. Salahuddin Ahmed & Bazlul Mobin Chowdhury
2. The History of Bengal (Vol.1 &Vol.2) : R.C. Majumdar
3. Banglapedia, 2003: Asiatic Society of Bangladesh
4. Bangladesh Arthaniti: Khan, Md. Shamsul Kabir
5. Bangladesh on the Threshold of the Twenty First Century, Asiatic Society of Bangladesh, 2002: A.M Chowdhury and Fakrul Alam
6. Poverty Reduction & Strategy, What, Why & for Whom , Asit Biswas et.al.(ed) Contemporary Issues in Development : M.M Akash
7. Bangladesh 2020, A longrun perspectives study: The World Bank

ECO 103 Principles of Economics 3 credits

A study of the fundamentals of micro and macroeconomics, nature and method of economics, individual markets, demand and supply, elasticity of demand and supply. Production and cost, market structures with special focus on perfect competition and monopoly, economic efficiency and market failure, determination of national income. The aggregate supply model, unemployment, inflation, unemployment-inflation tradeoff, government budget and fiscal policy, money creation and monetary policy, business cycles, economic growth, theory of comparative advantage, free trade versus protection, balance of payments and exchange rate policies.

Recommended Books:

1. Economics: John Solman
2. Principles of Macroeconomics: Robert H. Frank
3. Modern Economic Theory: K.K. Dewett
4. International Economics: D.R. Appleyard &A.J. Field

ENG 091 Foundation Course (Non-credit)

The English Foundation Course is designed to enable students to develop their competence in reading, writing, speaking, listening and grammar for academic purposes. The students will be encouraged to acquire skills and strategies for using language appropriately and effectively in various situations. The approach at all times will be communicative and interactive involving individual, pair and group work.

Recommended Books:

1. New Interchange, Student 's Book 3A, Cambridge University Press, 2002 : J. C. Richards, J. Hull, and S. Proctor.
2. Vocabulary Basics, Townsend Press, 1998: J. Nadel, B. Johnson, and P. Langan.
3. First steps in Academic Writing, Longman, 1996: A. Hogue
4. Get Ready to Write, Longman, 1998: K. Blanchard, C. Root.

ENG 101 English Fundamentals 3 credits

Developing basic writing skills: mechanics, spelling, syntax, usage, grammar review, sentence and essay writing.

Recommended Books:

1. Fundamentals of English: Jack C. Richards

ENG 102 Composition I 3 credits

The main focus of this course is writing. The course attempts to enhance students' writing abilities through diverse writing skills and techniques. Students will be introduced to aspects of expository writing: personalized/ subjective and analytical/persuasive. In the first category, students will write essays expressing their subjective viewpoints. In the second category students will analyze issues objectively, sticking firmly to factual details. This course seeks also to develop students' analytical abilities so that they are able to produce works that are critical and thought provoking.

Recommended Books:

1. Composition I: The Pearl; John Steinbeck

ENV 101 Introduction to Environmental Science 3 credits

Fundamental concepts and scope of environmental science, Earth's atmosphere, hydrosphere, lithosphere and biosphere, men and nature, technology and population, ecological concepts and ecosystems, environmental quality and management, agriculture, water resources, fisheries, forestry and wildlife, energy and mineral energy sources; renewable and non renewable resources, environmental degradation; pollution and waste management, environmental impact analysis, remote sensing & environmental monitoring.

Recommended Books:

1. Something New Under the Sun: An Environmental History of the TwentiethCentury World: J. R. McNeil & Paul Kennedy
2. Principles of Ecology: R Brewer
3. Fundamentals of Ecology: E. P. Odum

HUM 101 World Civilization and Culture 3 credits

A brief view of the major civilizations and cultural aspects in different continents covering ancient, medieval and modern civilizations. Topics include renaissance, reformation, and the beginning of the modern world, scientific revolution, industrial revolution, the age of democratic revolutions, nineteenth century Europe, Asia-Pacific Region, Africa, World Wars, South Asia: colonization, decolonization and after; contemporary world: Cold War and after.

Recommended Books:

1. World Civilization: Bums & others
2. Civilization: T Walter Walbank and others
3. A History of World Civilization: J. E. Swain
4. Western Civilization: : Robert E. Lerner & Standish Meachem

HUM 102 Introduction to Philosophy 3 credits

Philosophy: Concept of philosophy; science and philosophy; religion, literature and philosophy; sources of knowledge: empiricism, rationalism and criticism; concepts of value, ethics and sources of ethical standards.

Recommended Books:

1. A Modern Introduction to Philosophy: P Edwards and A. Pap
2. Philosophy: R. J. Hirst
3. Introduction to Modern Philosophy: C.E.M. Joad
4. An Introduction to Philosophical Analysis: J. Hospers
5. An Outline of Philosophy: A. Matin
6. Introduction of Philosophy: T. W. Patrick
7. Living Issues in Philosophy : H.H. Titus

HUM 103 Ethics and Culture 3 credits

This course introduces the students to principles and concepts of ethics and their application to our personal life. It establishes a basic understanding of social responsibility, relationship with social and cultural aspects, and eventually requires each student to develop a framework for making ethical decision in his work. Students learn a systematic approach to moral reasoning. It focuses on problems associated with moral conflicts, justice, the relationship between rightness and goodness, objective vs. subjective, moral judgment, moral truth and relativism. It also examines personal ethical perspectives as well as social cultural norms and values in relation to their use in our society. Topics include: truth telling and fairness, objectivity vs. subjectivity, privacy, confidentiality, bias, economic pressures and social responsibility, controversial and morally offensive content, exploitation, manipulation, special considerations (i.e. juveniles, courts) and professional and ethical work issues and decisions. On conclusion of the course, the students will be able to identify and discuss professional and ethical concerns, use moral reasoning skills to examine, analyze and resolve ethical dilemmas and distinguish differences and similarities among legal, ethical and moral perspectives.

Recommended Books:

1. Ethics, Culture and Psychiatry ­ International Perspectives: Ahmed Okasha, Julio Arboleda
2. Ethics and HRD: A New Approach to Leading Responsible Organizations: Tim Hatcher
3. The Ethical Challenge: How to Lead with Unyielding Integrity: Noel M. Tichy and Andrew
4. Dignity of Difference: How to Avoid the Clash of Civilizations: Jonathan Sacks
5. Culture and Ethics: Michel Labour, Charles Juwah, Nancy White and Sarah Tolley
6. Culture Matters: How Values Shape Human Progress: Samuel P. Huntington

HUM 111 History of Science 3 credits

This course will present a general overview of the development of scientific knowledge from ancient to modern times. It will examine how our modern scientific worldview developed over the ages in the fields of astronomy, physics, biology, chemistry, medicine, geology and other science disciplines. Focus will be on significant discoveries, the major scientists responsible for these revolutions, and the interrelation between science and society over the centuries. The course will contain the following: Science & philosophy, development of science in the ancient times, Greek & Egyptian science, science in the Orient, medieval science, science in the Islamic world, Western renaissance & industrialization, evolutionary theory, science in the modern ages. Science & religion, nature of scientific truth, validation of scientific theories.

Recommended Books:

1. Reader's Guide to the History of Science: A. Hessenbruch
2. Scientific Laws, Principles, and Theories: a Reference Guide: Robert E Krebs
3. The History of Science: an Annotated Bibliography: G Miller
4. A Guide to the History of Science: a First Guide for the Study of the History of Science, with Introductory Essays on Science and Tradition: G. arton
5. Knowledge & the World: Challenges Beyond the Science Wars: M. Cavrier, J. Roggenhofer, G. Kuppers & P. Blanclard
6. The Forgotten Revolution: How Science was Born in 300 BC and Why It Had to be Reborn: Lucio Russo
7. Hitler's Scientists: Science, War and the Devil's Fact: J. Cornwell

MAT 111: Principles of Mathematics 3 credits

Sets: Elementary idea of Set, Set notations, Set operations: union, intersection, complement, difference; Set operations and Venn diagrams. Set of Natural numbers, Integers, Rational numbers, Irrational numbers and Real numbers alongwith their geometrical representation, Idea of Open and Closed interval,. Idea of absolute value of real number, Variables and Constants, Product of two sets: Idea of product of sets, Product set of real numbers and their geometric representation, Axioms of real number system and their application in solving algebraic equations. Equation and Inequality, Laws of inequality, Solution of equations and inequalities. Variable and Functions: Variable of a set, Functions of single variable, Polynomial, Graph of Polynomial functions in single variable. Exponential, Logarithmic, Trigonometric functions and their graphs, Permutation and Combination. Binomial theorem.

Recommended Books:

1. Set Theory: Seymour Lipschutz.
2. Functions and Graphs : R. David Gustafson & Peter D. Frisk
3. Algebra and Trigonometry : Lial & Miller.
4. Calculus: Howard Anton.

MAT 121 Basic Algebra 3 credits

Elements of logic: Mathematical statements, Logical connectives, Conditional and biconditional statements, Truth tables and tautologies, Quantifications, Logical implication and equivalence, Deductive reasoning. The concept of sets: Sets and subsets, Set operations, Family of Sets. Relations and functions: Cartesian product of two sets, Relations, Order relation, Equivalence relations, Functions, Images and inverse images of sets, Injective, surjective, and bijective functions, Inverse functions. Real number system: Field and order properties, Natural numbers, integers and rational numbers. Absolute value, Basic inequalities. (Including inequalities of means, powers, Weierstrass, Cauchy) Complex number system: Field of complex numbers, De Moivre's theorem and its applications. Elementary number theory: Divisibility, Fundamental theorem of arithmetic, Congruence. Summation of finite series: Arithmetic-geometric series, Method of difference, Successive differences, Use of mathematical induction. Theory of equations: Synthetic division, Number of roots of polynomial equations, Relations between roots and coefficients, Multiplicity of roots, Symmetric functions of roots, Transformation of equations.

Recommended Books:

1. Set Theory : Seymour Lipschutz.
2. Higher Algebra : Shahidullah and Bhattacharjee.
3. Higher Algebra : Bernard and Child.
4. Higher Algebra : Md. Abdur Rahaman.

MAT 122 Analytic and Vector Geometry 3 credits

Two dimensional geometry
Coordinates: Cartesian and polar Coordinates, Transformations of coordinates and its applications. Reduction of second degree equations to standard forms, Pairs of straight lines, Circles, Identification of conics, Equations of conics in polar Coordinates.

Three dimensional geometry
Coordinates in three dimensions, Direction cosines, and Direction ratios. Planes, straight lines, shortest distance, sphere, orthogonal projection and conicoids.

Vector geometry
Vectors in plane and space, Algebra of vectors, scalar and vector products, Triple scalar products, its applications to Geometry.

Recommended Books:

1. Coordinate Geometry of Two Dimension : S. Loney.
2. Textbook on Coordinate Geometry : Rahman and Bhattacharjee.
3. Vector Analysis : Spiegel, M.R. Spiegel.
4. A Textbook on Coordinate Geometry and Vector Analysis: Khosh Mohammad.

MAT 123: Calculus I 3 credits

Differential Calculus: Real number system and its geometrical representation, real variable, function of single (real) variable, parametric equations, limit, continuity and differentiability, derivatives of different types of functions, geometrical significance of derivative, Rolle's Theorem, Mean Value Theorem, Taylor's Theorem; maxima, minima, point of inflexion, concavity and convexity, sketching of curves using concepts of calculus; Indeterminate Form, L'Hospital Rule, Successive Differentiation, Leibnitz's Theorem, tangent, normal and related formulas, curvature.

Integral Calculus: Indefinite integrals of different types of functions, various methods of integrations, definite integrals, Fundamental Theorems of Definite Integrals, properties of definite integrals, Reduction formulas, Arc Length, Area under the curves, Surface area and Volume of a 3-D objects. Improper Integrals and applications.

Prerequisite: MAT122

Recommended Books:

1. Calculus : Howard Anton.
2. Calculus and Analytical Geometry : Thomas Finney.
3. Calculus with Analytic Geometry : E.R. Swokowski.
4. Advanced Calculus : M.R. Spiegel.

MAT 124 Scientific Programming 3 credits

Problem-solving techniques using computers: Flowcharts, Algorithms, Pseudocode. Programming in FORTRAN: Syntax and semantics, data types and structures, input/output, loops, decision statements, arrays, user-defined functions, subroutines and recursion. Computing using FORTRAN: Construction and implementation of FORTRAN programs for solving problems in mathematics and sciences.

Recommended Books:

1. FORTRAN Programming : Schaum's Outline Series.

MAT 211 Calculus II 3 credits
Functions of several variables, concept of surface, sketching of , contour sketch for surface, limit and continuity, partial derivative and its geometrical significance, chain rule of partial differentiation, concept of gradient, divergence and curl, directional derivative and tangent plane, concept of differential and perfect differential, linear approximation and increment estimation, maxima, minima and saddle point, Lagrange multiplier, higher order derivatives, Taylor's theorem of function of several variables. Multiple integrals: Double integrals, Double integrals in Polar coordinates, Triple integrals, Triple integrals in Cylindrical and Spherical coordinates, Change of variables in Multiple integrals, Jacobian, Line integrals, Green's theorem, Surface integrals, Applications of Surface integrals, Divergence theorem, Stoke's theorem.

Prerequisite: MAT123.

Recommended Books:

1. Calculus : Howard Anton, Irl Bivens & Stephen Davis
2. Calculus and Analytical Geometry :Thomas Finney.
3. Calculus with Analytic Geometry : E.R. Swokowski.
4. Advanced Calculus : M.R. Spiegel.

MAT 212 Linear Algebra 3credits

Introduction to matrix, different types of matrices, equivalent matrices, determinants, properties of determinants, minors, cofactors, evaluation of determinants, adjoint matrix, inverse matrix, method for finding inverse matrix, elementary row operations and echelon form of matrix, system of linear equations (homogeneous and non-homogeneous equations) and their solutions; Vector, vector spaces and subspaces, linear independence and dependence, basis and dimension, change of bases, rank and nullity, linear transformation, kernel and images of a linear transformation and their properties, eigenvalues and eigenvectors, diagonalization, Cayley Hamilton theorem,

Recommended Books:

1. Elementary Linear Algebra and Applications: Howard Anton .
2. Linear Algebra : S. Lipschutz.
3. Linear Algebra : B. Kolman.

MAT 221 Real analysis I 3 credits

Real number system: Completeness of real numbers, supremum and infimum principles and their consequences, Dedekind's theorems, Bolzano-Weierstrass theorem. Sequences of Real Numbers: Infinite sequence, Convergent sequences, Monotone sequences, subsequences, Cauchy sequence, Cauchy criteria for convergence of sequences. Infinite Series: Concept of sum and convergence, series of positive terms, alternating series, absolute and conditional convergence, test for convergence, Convergence of sequences and series of functions. Continuity and Limits: Properties of continuous functions, Extreme Value Theorem and Intermediate Value Theorem, Uniform continuity concepts, Limits, Heine-Borel theorem. Integration: Necessary and sufficient conditions for integrability, Darboux Sums and Riemann Sums, Improper integral and their tests for convergence.

Recommended Books:

1. Principle of Mathematical Analysis : W. Rudin.
2. Real Analysis (3rd edition): H.L. Royden.
3. Mathematical Analysis: Tom .M. Apostol.
4. Real Analysis: A. Malik.

MAT 222 Differential Equations I 3 credits

Ordinary differential equations and their solutions: Classification of differential equations, Solutions, Implicit solutions, Singular solutions, Initial Value Problems, Boundary Value Problems, Basic existence and uniqueness theorems (statement and illustration only), Solution of first order equations: Separable equations, Linear equations, Exact equations, Special integrating factors, Substitutions and transformations, Modeling with first order differential equations, Model solutions and interpretation of results, Orthogonal and oblique trajectories, Solution of higher order linear equations: Linear differential operators, Basic theory of linear differential equations, Solution space of homogeneous linear equations, Fundamental solutions of homogeneous solutions, Reduction of orders, Homogeneous linear equations with constant coefficients, Non homogeneous equation, Method of undetermined coefficients, Variation of parameters, Euler Cauchy differential equation, Modeling with second order equations, Initial Value Problems and Boundary Value problems, reduction of order, Euler equation, generating functions, eigenvalue problems. Inhomogeneous linear difference equations (variation of parameters, reduction of order, Series solutions of second order linear equations: Taylor series solutions about an ordinary point. Frobenious series solutions about regular singular points. Series solutions of Legendre, Bessel, Laguerre and Hermite equations. Systems of linear first order differential equations: Elimination method. Matrix method for homogeneous linear systems with constant coefficients. Variation of parameters. Matrix exponential.

Prerequisite: MAT211

Recommended Books:

1. Introduction to Differential Equations : S.L. Ross.
2. Introduction to Differential Equations and Applications : D.G. Zill.
3. Differential Equations : Boyce & D'Prima.
4. Mathematical Methods (Volume I) : Md. Abdur Rahaman.

MAT 223 Numerical Analysis I 3 credits

Solution of equation of single variable: Fixed point iteration, Bisection algorithm, Method of False position, Newton-Raphson's method, Error Analysis for Iterative methods, Accelerating limit of convergence. Interpolation: Interpolating polynomials for equispaced and nonequispaced nodes, Lagrange's polynomial, Newton-Gregory's Interpolating polynomials, curve fitting with Least Square method, Iterated interpolation, Extrapolation. Differentiation and Integration: Numerical differentiation, Single point and (n+1)­point formulae of differentiation, Richardson's extrapolation, Numerical Integration, Gaussian quadrature formula, Trapezoidal, Simpson's, Weddle's Rules.

Prerequisite: MAT124

Recommended Books:

1. Numerical Analysis : R.L. Burden & J.D. Faires.
2. Applied Numerical Analysis : C.I. Gerald & P.O. Wheatly.
3. Introduction to Numerical Methods : S. Sastry.

MAT 311 Abstract Algebra 3 credits

Equivalence relation and residue classes modulo n. Groups and subgroups, Cyclic groups, Symmetric groups. Cosets and Lagrange's Theorem: Normal subgroups, Quotient groups, Permutation groups, Homomorphism, Isomorphism and Automorphism of groups with related theorems and problems, Cayley's Theorem, centralizer and normalizer of an element/ subset in a group. Rings, Ideals, and Quotient Rings, Prime and Maximal Ideals. Integral Domain, Field of fractions. Principal Ideal Domain, Euclidian Domain, Unique Factorization Domain.
Polynomial Rings, Primitive polynomials, Gauss Theorem, Eisenstein's criterion for irreducibility. Prime Fields, characteristic of Fields.

Prerequisite: MAT121

Recommended Books:

1. Topics in Algebra: Herstein.
2. First Course in Abstract Algebra: J.B. Frayleigh.
3. A First Course in Abstract Algebra: H. Paley & P.M. Weicheel.
4. Modern Algebra : R.S. Aggarwal.

MAT 312 Numerical Analysis II 3 credits

Part A: Theory
Solutions of linear system of equations: Gaussian Elimination method with pivoting, Matrix inversion, Direct factorization of matrices, Iterative Techniques for solving linear system of equations: Jacobi's and Gauss-Seidel Method. Solution of tridiagonal system, Eigen values and Eigen vectors (Power Method). Numerical solution of Nonlinear system: Fixed point for functions of several variables, Newton's method, Quasi-Newton's method. Initial Value Problem for ODE: Euler's method, Higher order Taylor's method, Runge-Kutta methods, Multistep methods, Variable Stepsize Multistep methods. Boundary Value Problem: Linear Shooting method, Shooting method for non linear BVP. Boundary Value problem involving elliptic, parabolic and hyperbolic equations, explicit and implicit Finite Difference method.
Part B: Numerical Analysis Lab
Construction and implementation of FORTRAN / C, C++ programs of techniques in Numerical Analysis. There will be at least 15 lab assignments.

Prerequisite: MAT 223

Recommended Books:

1. Numerical Analysis, Brooks/cole : R.L. Burden & J.D. Faires.
2. Applied Numerical Analysis : C.I. Gerald & P.O. Wheatly.
3. Numerical Recipes in FORTRAN : W.H. Press, S.A. Teukolsky, W.T. Vetterling & B.P. Flannery.
4. Numerical Solution of Partial Differential Equations: G.D. Smith.

MAT 313 Differential Geometry 3 credits

Curves in space: Vector functions of one variable, space curves, unit tangent to a space curve, equation of a tangent line to a curve, Osculating plane (or plane of curvature), vector function of two variables, tangent and normal plane for the surface , Principal normal, binormal and fundamental planes, curvature and torsion, Serret Frenet's formulae, theorems on curvature and torsion, Helices and its properties, Circular helix. Spherical indicatrik, Curvature and torsion. Curvature and torsion for spherical indicatrices. Involute and Evolute of a given curve, Bertrand curves. Surface: Curvilinear coordinates, parametric curves, Metric (first fundamental form), geometrical interpretation of metric, relation between coefficients E, F, G. properties of metric, angle between parametric curves, elements of area, second fundamental form. Derivatives of surface normal M (Weingarten equations), Third fundamental form, Principal sections, Principal sections, direction and curvature, first curvature, mean curvature, Gaussian curvature, normal curvature, lines of curvature, centre of curvature, Rodrigues's formula, condition for parametric curves to be line of curvature, Euler's Theorem, Elliptic, hyperbolic and parabolic points, Dupin Indicatrix.

Recommended Books:

1. Vector Analysis: Spiegel
2. Differential Geometry: Henderson
3. Foundations of Differential Geometry: S. Kobayashi, Katsumi Nomizu
4. Differential Geometry : Lipschutz , McGraw Hill

MAT 314 Complex Analysis 3 credits

Introduction to complex numbers and their properties, complex functions, limits and continuity of complex functions, Analytic functions, Cauchy Riemann equations, harmonic functions, Rational functions, Exponential functions, Trigonometric functions, Logarithmic functions, Hyperbolic functions. Contour integration: Cauchy's Theorem, Simply and Multiply connected domain, Cauchy integral formula, Morera's theorem, Liouville's theorem. Convergent series of analytic functions, Laurent and Taylor series, Zeroes , Singularities and Poles, residues, Cauchy's Residue theorem and its applications, Conformal Mapping.

Prerequisite: MAT123

Recommended Books:

1. Complex Analysis and Applications: Churchill & Brown.
2. Complex Analysis : M.R. Spiegel.

MAT 315 History of Mathematics 3 credits

A Survey of the development of mathematics beginning with the history of numeration and continuing through the development of the calculus. The study of selected topics from each field is extended to the 20th century. Biographical and historical aspects will be reinforced with studies of procedures and techniques of earlier mathematical cultures.

Recommended books:

1. A History of Mathematics; CB Boyer, UC Merzbac; Wiley.
2. The History of Mathematics; VJ Katz; AddisonWesley.
3. A Short Account of the History of Mathematics; WWR Bell; Macmillan.

MAT 316 Operations Research I 3 credits

Convex sets and related theorems, Introduction to linear programming, Formulation of linear programming problems, Graphical solutions, Simplex method, Duality of linear programming and related theorems, Sensitivity. Unconstrained optimization: Newton's method, Trust region algorithms, Least Squares and zero finding. Constrained optimization: linear/nonlinear
equality/inequality constraints, Duality, working set methods. Linear programming: Simplex method, primal dual interior point methods.

Recommended Books:

1. Operations Research: An Introduction ,4th Edition by Hamdy A. Taha
2. Convex Optimization: Stephen Boyd & Lieven Vandenberghe
3. Schaum's Outline of Operations Research by Richard Bronson.

MAT 321 Real Analysis II 3 credits

Metric spaces: definition and some examples, open sets, closed sets, Convergence, Completeness, Baire's theorem. Connected set: Compact sets, locally compact sets and related theorems, connected sets, locally connected sets, continuity and compactness. Sequence in metric space: Convergent and Cauchy sequence, Completeness, Banach Fixed Point theorem with applications, sequence and series of functions, pointwise and uniform convergence, differentiation and integration of series. Continuous function on metric space: Boundedness, Intermediate Value Theorem, uniform continuity. Differentiation in N : Jacobian , implicit and inverse function theorems. Integration in N : contents and integrals, Fubini's theorem, change of variables.

Prerequisite: MAT221

Recommended Books:

1. Principle of Mathematical Analysis: W. Rudin.
2. Real Analysis (3rd edition) : H.L. Royden.
3. Mathematical Analysis: Tom .M. Apostol.
4. Real Analysis: A. Malik.
5. Mathematical Analysis: K.G. Binmore.

MAT 322 Differential Equations II 3 credits

ODE: Existence and uniqueness theory: Fundamental existence and uniqueness theorem. Dependence of solutions on initial conditions and equation parameters. Existence and uniqueness theorems for systems of equations and higher order equations. Eigen value problems and Strum-Liouville boundary value problems: Regular Strum-Liouville boundary value problems. Solution by eigenfunction expansion. Green's functions. Singular Strum-Liouville boundary value problems. Oscillation and comparison theory. Nonlinear differential equations: Phase plane, paths and critical points. Critical points and paths of linear systems.

PDE: First order equations: complete integral, General solution. Cauchy problems. Method of characteristics for linear and quasilinear equations. Charpit's method for finding complete integrals. Methods for finding general solutions. Second order equations: Classifications, Reduction to canonical forms. Boundary value problems related to linear equations. Applications of Fourier methods (Coordinates systems and separability. Homogeneous equations.) Boundary value problems involving special functions. Transformation methods for boundary value problems, Applications of the Laplace transform. Application of Fourier sine and cosine transforms.

Prerequisite: MAT222.

Recommended Books:

1. Introduction to Differential Equations: L. Ross
2. Partial Differential Equation, SpringerVerlag: F. John:
3. Differential Equations: Boyce & D'Prima
4. Mathematical Methods : B.D. Gupta.
5. Differential Equations, McGrawHill: Sneddon.
6. Introduction to Partial Differential Equations: K. Sankara Rao.
7. Mathematical Methods (Volume II) Md. Abdur Rahaman

MAT 323 Dynamical Systems 3 credits

Statics: Fundamental concept and principle of Mechanics. Statics of Particles: Review of vectors, vector addition of forces, resultant of several concurrent forces, resolution of forces into components, equilibrium of particles in a plane and in space. Rigid bodies: momentum of a force and a couple, Varignon's theorem, equivalent system of forces and vectors, reduction of system of forces. Equilibrium of rigid bodies: reactions at supports and connections of rigid bodies in two dimensions. Centroid and center of gravity: CG of two and three dimensional bodies, centroids of areas, lines and volumes. Moment of inertia, moments and products of inertia, radius of gyration, parallel axis theorem, principal axis and principal moments of inertia.

Dynamics: Kinematics of particles: rectilinear and curvilinear motion of particles. Kinematics of particles: Newton's second law of motion, linear and angular momentum of a particle, conservation of energy and momentum, principle of work and energy and their applications, motion under a central force and conservative central force, impulsive motion. System of particles: Newton's law, effective forces, linear and angular momentum, conservation of momentum and energy, work energy principle. Kinematics of rigid bodies: translation, rotation, and plane motion relative to rotating frame, Coriolis force. Plane motion of a rigid body: motion in two dimensions, Euler's equation of motion about a fixed point.

Prerequisite: MAT122.

Recommended Books:

1. Vector Mechanics for Engineers: F.P. Beer & E.R. Johnston.
2. Principle of Mechanics : Soynge & Griffiths.

MAT 324 Graph Theory 3 credits

Number System: Numbers with different bases, their conversion and arithmetic operations, normalized scientific notations. Logic: Introduction to logic, logical operations, application of logic to sets. Mathematical Reasoning: Methods of proof, Mathematical induction, recurrence relations, generating functions. Boolean Algebra: Ordered sets, lattices, Boolean algebra and operations, Boolean expressions, logic gates, minimization of Boolean expressions, Karnaugh maps, Karnaugh map algorithm. Graphs: introduction and definitions, representing graphs, graph isomorphism, connected graph, planar graph, path and circuit, shortest path algorithm, Eulerian path, Euler's theorem, Seven Bridges of Problem, graph coloring. Application of graph: tree, tree reversal, trees and sorting, spanning trees, minimum spanning trees: related algorithms. Search trees: binary search tree, leaves on a rooted tree, spanning trees and the MST problems, network and flows, the max flow and the min-cut theorem. Binary trees.

Recommended Books:

1. Discrete Mathematics & its Applications: K.H. Rosen.
2. Discrete Mathematics, Oxford : N.L. Biggs.
3. Graph Theory, Coding Theory & Block Design, Cambridge: P.J. Cameron & J.H. Van Kaint.
4. Discrete and Combinational Mathematics : Ralph P. Grimaldi.

MAT 325 Mathematical Methods 3 credits

Series solution: singularity of a rational function, series solution of linear differential equations at nonsingular and regular singular points. Fourier series: Introduction to orthogonal functions and Integral transform, Fourier integral, Fourier transform and their applications. Laplace transformation method: Definition, existence and properties of Laplace transform, Inverse Laplace transform, Transforms of discontinuous and periodic functions. Convolution. Impulses and Dirac delta function. Solving initial value problems. Solving linear systems, Harmonic functions: Laplace equation in different coordinates and its applications. Special functions: Legendre functions of first and second kinds, Hermite polynomials, generating function, Hypergeometric functions, Laguerre functions, Bessel function and their properties.

Prerequisite: MAT 322

Recommended Books:

1. Fourier Series and Boundary Value Problem : Churchill & Brown.
2. Introduction to Differential Equations, Eddison Wesley: L. Ross.
3. Mathematical Methods: B.D. Gupta.
4. Mathematical Methods : Abdur Rahman.
5. Laplace Transform : M.R. Spiegel.

MAT 326 Hydrodynamics 3 credits

Preliminaries: Concept of viscosity; Inviscid fluid; stream line, path line and streak lines; steady and unsteady motion. Equation of motion: Equation of continuity; Euler's equation of motion, conservative forces, Bernoulli's equation; circulation and Kelvin's circulation theorem; vorticity, irrotational and rotational motion, velocity potential; energy equation, Kelvin's minimum energy theorem. Two dimensional motion: vorticity, stream function and velocity potential function, streaming motion, complex potential and complex velocity, stagnation points, motion past a circular cylinder, circle theorem, motion past a cylinder, Joukowaski transformation, Blasius theorem; two dimensional source, sink and doublets, source and sink in a stream, the method of image. Vortex motion: vortex line, tube and filament, rectilinear and circular vortices, kinetic energy of system of vortices, vortex sheet, Karman's vortex street.

Recommended Books:

1. Fluid Dynamics : F. Chorlton.
2. Theoretical Hydrodynamics: L.M. Milne Thompson.
3. Hydrodynamics : H. Lamb.
4. Hydrodynamics : P.P. Gupta.

MAT 411 Topology 3 credits

Metric Spaces: Definition and some examples. Open sets. Closed sets. Convergence. Completeness. Baire's theorem. Continuous mappings. Spaces of continuous functions. Euclidean and unitary spaces. Topological Spaces: Definition and some examples. Elementary concepts. Open bases and open subbases. Weak topologies. Function algebras. Compactness: Compact spaces. Product spaces. Tychonoff's Theorem. Locally compact spaces. Compactness for metric spaces. Separation: T1-spaces and Hausdorff spaces. Completely regular spaces and normal spaces. Urysohn's lemma. Connectedness: Connected spaces. Locally connected spaces. Pathwise connectedness. Banach Spaces: Definition and some examples. Continuous linear transformations. Hahn-Banach theorem. Natural embedding. Open mapping theorem. Conjugate of an operator. Hilbert Spaces: Definition and some simple properties. Orthogonal complements. Orthogonal sets. Conjugate spaces. Adjoint and self-adjoint operators. Fixed point theory: Banach contraction principle. Schauder Principle. Applications.

Prerequisite: MAT 221

Recommended Books:

1. Introduction to Topology & Modern Analysis: G.I. Simmons.
2. General Topology : S. Lipschutz.
3. General Topology : J.K. Killey.

MAT 415 Finite Element Methods 3 credits
Basic concept of finite element method, approximate solution of BVP, direct approach to Finite Element Methods. Galerkin's weighted residual method for one-dimensional BVP, the modified Galerkin's technique. Shape functions for one-dimensional elements. Division of a region into elements, linear and quadratic elements, numerical integration over elements. Finite element solution of one dimensional BVPs. Finite Element approximations of line and double integrals: line integral using quadratic elements, double integrals using triangular and quadrilateral elements, double integrals using curved elements. Finite Element solution of two-dimensional BVP: Galerkin formulation, matrix formulation for 2-D finite elements. Three-nodded triangular elements. Variational formulation of BVP: construction of variational functions, the Ritz method and finite elements, matrix formulation of the Ritz procedure, solution of two-dimensional problems. Pre-processing and solution assembly: mesh generation in one and two dimensions, techniques of assembly and solutions.

Prerequisite: MAT312.

Recommended Books:

1. Finite Element Analysis for Undergraduates : E.Akin.
2. The finite Element Method: Principles and Applications, P.E. Lewis and J.P Ward.
3. The Finite Element Method in Engineering : S.S.Rao.
4. Application and implimentation of Finite Element Methods, J.E.Akin.

MAT 416 Tensor Calculus 3 credits

Tensor: Coordinates, Vectors and tensors: Curvilinear coordinates, Kronecker delta, summation convention, space of N dimensions, Euclidean and Riemannian space, coordinate transformation, Contravariant and covariant vectors, the tensor concept, symmetric and skewsymmetric tensor. Riemannian metric and metric tensors: Basis and reciprocal basis vectors, Euclidean metric in three dimensions, reciprocal or conjugate tensors, Conjugate metric tensor, associated vectors and tensor's length and angle between two vector's, The Christoffel symbols. Covariant Differentiation of Tensors and applications: Covariant derivatives and its higher rank tensor and covariant curvature tensor.

Prerequisite: MAT313

Recommended Books:

1. Introduction to Tensor Calculus and Continuum Mechanics: J.H. Heinbockel
2. Tensor Analysis : Richard L Bishop
3. A Brief on Tensor Analysis : James G. Simmonds
4. Tensor Analysis : J.L. Synge
5. Tensor Analysis : Md. Abdur Rahaman.

MAT 421 Fluid Mechanics 3 credits

Preliminaries: Real and ideal fluids, Viscosity, Reynolds number, laminar and turbulent flows, boundary layers. Stress and rate of strain, General stress state of deformable bodies, General state of deformation of flowing fluid, Relation between stress and rate of deformation in general orthogonal coordinates. Equations of motion: Thermodynamic equation of state, Equation of continuity, Navier-Stokes equations, Energy equation, Equations of motion in different coordinate system. Exact solution of Navier-Stokes equations, Steady plane flow, Couette-Poiseuille flow, Plane stagnation-point flow, flow past parabolic body and circular cylinder, Steady axisymmetric flow, Circular pipe flow (Hagen-Poiseuille flow), Flow between two concentric rotating cylinders, Flow at a rotating disc, Unsteady plane flow, First Stokes problem, Second Stokes problem, Startup of Couette flow, Unsteady plane stagnation-point flow. Similarity analysis: Reynolds law of similarity, Dimensional analysis and theorem, Important non-dimensional quantities. Very slow motion: Equations of slow motion, Motion of a sphere in a viscous fluid, Theory of lubrication. Laminar boundary layer: Introduction to boundary layer, boundary layer equations in two dimensions, Dimensional representation of boundary layer equations, Displacement thickness, Friction drag, Flat plate boundary layer, Momentum thickness, Energy thickness, Similar solutions of boundary layer equations: Derivation of ODE, Wedge flow, Flow in a convergent channel, Integral relations of the boundary layer: Momentum-Integral equation, Energy-Integral equation.

Prerequisite: MAT 326

Recommended Books:

1. Boundary Layer Theory : Schilisting
2. Introduction to Fluid Dynamics : G. Taylor
3. Fluid Mechanics : F. Chorlton
4. Fluid Mechanics : Raisinghania

MAT 422 Theory of Numbers 3 credits

Arithmetic in U. Euclidean algorithm. Continued fractions. The ring U and its group of units. Chinese Remainder Theorem. Linear Diophantine equations. Arithmetical functions. Dirichlet convolution. Multiplicative function. Representation by sum of two and four squares. Arithmetic of quadratic fields. Euclidean quadratic Fields.

Recommended Books:

1. Theory of Numbers: G.H. Hardy & E.M. Wright.
2. Theory of Numbers : Niven & Zucherman.
3. Theory of Numbers: J. Hunter.
4. Theory of Numbers : Apostol.

MAT 423 Mathematical Modeling 3 credits

Modeling in Biology
Continuous population models for single species: Continuous growth models, Delay models, Periodic fluctuations, Harvesting models. Discrete population models for single species: Simple models, Cobwebbing, Discrete logistic models, Stability, Periodic fluctuations and Bifurcations, Discrete Delay models, Continuous models for interacting populations: Predator-prey models, Lotka-Volterra systems, Complexity and stability, Periodic behaviour, Competition Models, Mutualism. Discrete growth models for interacting populations: Predator-prey models. Epidemic models and dynamics of infectious diseases: Simple epidemic models and practical applications.

Modeling in Economics
Theory of the household: Preference and indifference relations, Utility function, Order conditions of optimization, Stutsky equation, Demand functions, Revealed Preference hypothesis, Von Neumann-Morgenstern utility. Theory of the firm: Production function, Laws of production and scale, Optimizing behaviour, Cost curves and cost functions, Constrained output maximization. Theory of factor demand: Optimal input mix, Factor demand and supply curves, Elasticity of derived demand. Market structures and equilibrium: Market Economy and equilibrium, Stability of equilibrium, Dynamic stability.

Prerequisite: MAT 322.

Recommended Books:

1. The Nature of Mathematical Modeling, Cambridge University Press: Gerschenfeld.
2. An Introduction to Mathematical Modeling, Dover Publication: F.A. Bender.
3. A First Course in Mathematical Modeling, Brooks/cole: F.R. Giordano & M.D. Weir.
4. Guide to Mathematical Modeling, MacMillan: D. Edwards & M. hamson.

MAT424 Operations Research II 3 credits

Transportation and Assignment Problem: Introduction and formulation; relationship with linear programming. Network models: shortest route problems, minimal spanning, maximal-flow problem. Sequencing problem: Minimax-maximin strategies, mixed strategies, expected pay-off, solution of and games, games by linear programming and Brown's algorithm. Dynamic programming: Investment problem, Production Scheduling problem, Stagecoach problem, Equipment replacement problem. Non-linear programming: Introduction, unconstrained problem, Lagrange method for equality constraint problem, Kuhn-Tucker method for inequality constraint problem. Quadratic programming.

Prerequisite: MAT 316

Recommended Books:

1. Operations Research: An Introduction ,4th Edition by Hamdy A. Taha
2. Convex Optimization: Stephen Boyd & Lieven Vandenberghe
3. Schaum's Outline of Operations Research by Richard Bronson

MAT 425 Advanced Numerical Methods 3 credits

Non-iterative (Newton's, steepest descent) methods for solution of a system of equation(linear and non-linear). Approximation theory: discrete least square applications, Chebyshev polynomial applications, rational function approximation, trigonometric polynomial approximation, Fast Fourier Transform. Approximating Eigenvalues: Honseholder's method, QR algorithm. BVP involving ODE: shooting method for linear and nonlinear problems, finite difference method for linear and nonlinear problems. PDE: Finite difference methods for elliptic, parabolic and hyperbolic problems.

Prerequisite: MAT 312

Recommended Books:

1. Advanced Methods for Scientists and Engineers, Mc.GrawHill Int: C.M. Bender and S.A. Orszag.
2. Asymptotic Expansions for Ordinary Differential Equations Wiley, New York, 1965.; W.A. Wasow.
3. Introduction to Nonlinear differential and Integral Equations Dover Publications: H.T Davis.

MGT 211 Principles of Management 3 credits

Meaning and importance of management, evolution of management thoughts; managerial decision making; Environmental impact, corporate social responsibility, planning, setting objectives, implementing plans, organizing; organization design, managing change, directing, motivation, leadership, managing work groups, controlling: principles, process and problems and managers in changing environment.

Recommended Books:

1. Management: Stephen P. Robbins and Mary Coulter
2. Management: James A. F. Stoner, Edward R. Freeman & Daniel R. Gilbert

PHY 111 Principles of Physics I 3 Credits

Vectors and scalars, unit vector, scalar and vector products, static equilibrium, Newton's Laws of motion, principles of conservation of linear momentum and energy, friction, elastic and inelastic collisions, projectile motion, uniform circular motion, centripetal force, simple harmonic motion, rotation of rigid bodies, angular momentum, torque, moment of inertia and examples, Newton's Law of gravitation, gravitational field, potential and potential energy. Structure of matter, stresses and strains, Moduli of elasticity Poison's ratio, relations between elastic constants, work done in deforming a body, bending of beams, fluid motion and viscosity, Bernoulli's Theorem, Stokes' Law, surface tension and surface energy, pressure across a liquid surface, capillarity. Temperature and Zeroth Law of thermodynamics, temperature scales, isotherms, heat capacity and specific heat, Newton's Law of cooling, thermal expansion, First Law of thermodynamics, change of state, Second Law of thermodynamics, Carnot cycle, efficiency, kinetic theory of gases, heat transfer. Waves & their propagation, differential equation of wave motion, stationary waves, vibration in strings & columns, sound wave & its velocity, Doppler effect, beats, intensity & loudness, ultrasonics and its practical applications. Huygens' principle, electromagnetic waves, velocity of light, reflection, refraction, lenses, interference, diffraction, polarization.

Recommended Books:

1. Fundamentals of Physics: D. Halliday, R. Resnick & J. Walker
2. University Physics: Francis W. Sears, Mark W. Zemansky, Hugh D. Young
3. Theory & Problems of Vector Analysis: Schaum's Outlines
4. Outlines of Physics Vol.1: Dr. Giasuddin Ahmad
5. Properties of Matter: Brij Lai and N. Subrahmanym
6. Heat and Thermodynamics: Brij Lai and N. Subrahrnanyam
7. A Textbook of Sound: N. Subrahmanyam and Brij Lal
8. A Textbook of Optics : Brij Lal and N. Subrahrnanyam

PHY 112 Principles of Physics II 3 Credits

Electric charge, Coulomb's Law, electric field & flux density, Gauss's Law, electric potential, capacitors, steady current, Ohm's law, Kirchhoff's Laws. Magnetic field, BiotSavart Law, Ampere's Law, electromagnetic induction, Faraday's Law, Lenz's Law, self inductance and mutual inductance, alternating current, magnetic properties of matter, diamagnetism, paramagnetism and ferromagnetism. Maxwell's equations of electromagnetic waves, transmission along wave guides. Special theory of relativity, length contraction and time dilation, massenergy relation. Quantum theory, Photoelectric effect, xrays, Compton effect, dual nature of matter and radiation, Heisenberg uncertainty principle. Atomic model, Bohr's postulates, electron orbits and electron energy, Rutherford nuclear model, isotopes, isobars and isotones, radioactive decay, halflife, alpha, beta and gamma rays, nuclear binding energy, fission and fusion.Fundamentals of solid state physics, lasers, holography.

Recommended Books:

1. Fundamental of Physics: D. Halliday, R. Resnick and J. Walker
2. University Physics: Francis W. Sears, Mark W. Zemansky, Hugh D. Young
3. Electricity and Magnetism with Electronics: K.K. Tewari
4. B.Sc. Physics Volume 1: C.L. Arora
5. Perspectives of Modern Physics: A. Beiser

PHY 204 Classical Mechanics and Special Theory of Relativity 3 credits

Classical Mechanics: Newtonian equations of motion, conservation laws of a system of particles, variable mass, generalized coordinates, generalized force, D' Alembert's Principle, variational method, EulerLagrange equations of motion, Hamilton's principles, twobody central force problem, elliptic orbit, scattering in a central field, Rutherford formula, kinematics of rigid body motion, Euler angles, rotating coordinates, Coriolis force, wind motion, principal axis transformation, top motion, principle of least action, Hamiltonian equations of motion, small oscillations, normal coordinates, normal modes. Special Theory of Relativity: Galilean relativity, MichelsonMorley experiment, postulates of special theory of relativity, Lorentz transformation, length contraction, time dilation, twin paradox, variation of mass, relativistic kinematics, mass energy relation.

Recommended Books:

1. Classical Mechanics: H. Goldstein
2. Special Relativity: A.P. French
3. Perspectives of Modern Physics: A. Beiser
4. Special Relativity from Einstein to Strings: Patricia Schwarz
5. An Introduction to Special & General Relativity: Hans Stephain

PHY 205 Statistical Mechanics 3 Credits

Statistical Mechanics: Phase space, concept of state and ensemble, microcanonical, canonical and grand canonical ensembles, Boltzmann probability distribution, Maxwell velocity distribution, derivation of Bose-Einstein and Fermi-Dirac statistics, ideal Fermi gas, degenerate Fermi system, equation of state of ideal gases, ideal Bose gas, application of Statistical mechanics in various fields in physical, biological, social sciences, economics, finance and in engineering & ICT.

Recommended Books:

1. Fundamentals of Statistical and Thermal Physics: F. Reif
2. Statistical Mechanics: Kerson Huang
3. Statistical Physics: F. Mandl
4. Elementary Statistical Physics: C. Kittel

PHY 303 Quantum Mechanics I 3 Credits

Breakdown of classical physics, quantum nature of radiation, Planck's Law, photoelectric effect, Einstein's photon concept and explanation of photoelectric effect, Compton Effect, de Broglie wave, wave particle duality, electron diffraction, DavissonGermer experiment, emergence of quantum mechanics, Schrodinger equation, basic postulates of quantum mechanics, physical interpretation of wave function, wave packets, Heisenberg's uncertainty principle, linear operators, Hermitian operators, eigenvalue equation, onedimensional potential problem, harmonic oscillator, orbital angular momentum, rotation operator, spherical harmonics, spin angular momentum, spherically symmetric potential, solution of the Schrodinger equation for hydrogen atom, matrix formulation of quantum mechanics.

Recommended Books:

1. Quantum Mechanics: John L. Powell and B. Craseman
2. Quantum Mechanics: L.I. Schiff
3. Quantum Mechanics: E. Merzbacher
4. Quantum Mechanics: A.M. Harun ar Rashid
5. Introduction to Quantum Mechanics: P.T. Matthews
6. Modern Quantum Mechanics: J.J. Sakurai
7. Quantum Mechanics: D.R. Bes

PHY 312 Physics for Development 3 Credits

Twenty first century development issues, physics and break through technologies, ICT, fibre optics, quantum information theory, physics in genetics engineering and molecular biology, physics and health issues, bio and medical physics, materials science and physics, high temperature superconducting materials, space physics, microgravity experiments, onophysics,
physics principles applied in sociology.

Recommended Books:

1. Oxford Companion to the History of Modern Science: J.L. Heilbron.
2. The Evolution of Technology (Cambridge Studies in the History of Science): George Basalla & Owen Hannaway
3. Technology in World Civilization: A ThousandYear History: Arnold Pacey
4. Zoological Physics: B.K. Ahlborn
5. New Directions in Statistical Physics: Econophysics, Bioformatics & Pattern Reorganization: L.T. Willie
6. Knowledge & the World: Challenges Beyond the Science Wars: M. Cavrier, J. Roggenhofer, G. Kuppers & P. Blanchard

PHY 413 General Theory of Relativity 3 Credits

Gravitation, Lagrangian Einstein equations, approximation of weak field and Hilbert's auxiliary conditions, comparison of corresponding relations with those of Newton's theory of gravitation, source of gravitation field, Schwarzschild's solution in isotropic and other coordinate systems, analogy between gravitation and electromagnetism, motion of test mass and geodetic lines, motion in Schwarszchild's field, equations of motion in general relativistic mechanics as a consequence of Einstein's equation of gravitational field, gravitational waves in weak field approximation, problem of energy transfer, exact wave solutions in the case of gravitational field, waves of matrices or wave of curvature, locally plane gravitational waves, Weber's and Braginski's experiments, prospects of future gravitational experiments.

Recommended Books:

1. A First Course in General Relativity: Bernard F. Schutz
2. Gravitation and Cosmology: Steven Weinberg
3. General Relativity: Robert Wald
4. Relativity: Foster
5. Relativity & Cosmology: J.N. Islam
6. An Introduction to Special & General Relativity: Hans Stephain

POL 103 Introduction to Political Science 3 Credits

A study of political systems and process with special reference to Bangladesh. Topics include nature and origin of state, sovereignty of state, forms of political units, liberty, law, process of politics, political structure, political ideas democracy, socialism, nationalism, peoples' behaviour in politics. Political system, process and problems of Bangladesh.

Recommended Books:

1. A History of Political Thought: Plato to Marx: Subrata Mukherjee & Sushila Ramaswamy
2. An Introduction to Political Science: Rand Dyck
3. A Social Political History of Bengal and the Birth of Bangladesh: Kamruddin Ahmed
4. Radical Politics and the Emergence of Bangladesh: Talukder Manizzaman
5. India and Pakistan: A Political Analysis: Hugh Tinker
6. Politics and Policy Making in Developing Countries: Perspective on the New Political Economy: Gerald M. Meier
7. Political Culture, Political Parties and Democratic Transition in Bangladesh: Shamsul I. Khan, S. Aminul Islam & Imdadul Haque
8. Involvement in Bangladesh's Struggle for Freedom: T. Hossain
9. History of Bangladesh 17041971: Political History: Sirajul Islam
10. Conflict and Compromise: An Introduction to Political Science: H.R. Winter

POL 245 Women, Power & Politics 3 Credits

A critical examination of the impact of gender on forms and distributions of power and politics, with primary reference to the experience of Women in South Asia. Three major concerns will be addressed. First, what do we: mean by "sex", "gender". "women", "power" and "politics"? Second, how do issues of class and race/ethnicity inform our understanding of women and politics? Third, what is the relationship between women and the state? How can women organise collectively to challenge state policies, how does the state respond to organised women?

Prerequisite: POL 103

Recommended Books:

1. The Elusive Agenda: Mainstreaming Women in Development, UPL: Raunaq Jahan.
2. Persistent Inequalities: Women and World Development, 1990: Frene Tinker
3. Women Leaders in Development Organizations and Institutions: Sayeda Rawsan Kadir.
4. Population Policy and Women Rights: Transforming Reproductive Choice: Prayer, Ruth DixonMueller.
5. Women in Politics, 1994, Dhaka Women for Women: Najma Chowdhury, Hamida A Begum, Mahmuda Islam and Nazmunnessa Mahtab.

PSY 101 Introduction to Psychology 3 Credits

The objective of this course is to provide knowledge about the basic concepts and principles of psychology pertaining to reallife problems. The course will familiarize students with the fundamental process that occur within organismbiological basis of behaviour, perception, motivation, emotion, learning, memory and forgetting and also to the social perspectivesocial perception and social forces that act upon the individual.

Recommended Books:

1. Introduction to Psychology: C.T. Morgan
2. Introduction to Psychology: R.F. Crider
3. Understanding Psychology: Robert Feldman

SOC 101 Introduction to Sociology 3 credits

Perspectives on society, culture, and social interaction, Topics include community, class, ethnicity, family, sex roles, and deviance. Social problems and sociological problems. Problems, theories, and the nature of sociological explanation. Explanation, evidence and objectivity. Sociology as a comparative study of social action and social systems. Some models of sociological thinking as applied to the study of the following: aspects of social ranking; forms of interpersonal and personal relationships; the changing nature of the relationship between economy and society; the sociology of development; the origins and spread of capitalism and socialism; ideology and belief systems; religion and society; rationality and nonrationality; conformity and deviance.

Recommended Books:

1. Sociology: Anthony Giddens
2. Sociology: Richard T. Schaefer
3. Sociology: Rao and C.N. Shankar
4. Sociology: Neil J. Smelser

SOC 401 Gender and Development 3 credits

Position & role of women in society, contemporary issues, analysis of various aspects of gender relations, gender discrimination, societal attitude, different forms of feminism, women in higher education, employment of women & discrimination, workplace harassment, contribution of women in development: world picture I position in Bangladesh.

Prerequisite: SOC 101

Recommended Books:

1. Women and Social Security: Progress Towards Equality of Treatment, 1990 Geneva International Labor Office: Anne Marie Brocas, AnneMarie Cailloux and Virgine Oget.
2. Impact of Women in Development Projects on Women Status and Fertility in Bangladesh, 1993, Dhaka, Development Researchers and Associates: M. Kabir, Rokeya Khatun, Ishrat Ahmed.
3. Integration of Women in Development: Why, When and How: Ester Boseup, Cristine Liljencrantz.
4. Women in the Third World: Gender Issue in Rural and Urban areas: Hants
5. Women, Man and Society: The Sociology of Gender: Allyn and Bacon, Claire M Renzetti, Daniel J Curran.
6. Race, Ethnicity, Gender and Class: the Sociology of Group Conflict and Change, London: Joseph F Healey

STA 201 Elements of Statistics and Probability 3 credits

Frequency distribution, mean, median, mode and other measures of central tendency, standard deviation and other measures of dispersion, moments, skewness and kurtosis, elementary probability theory and discontinuous probability distribution, binomial, Poisson and negative binomial distribution, continuous probability distributions, normal and exponential, characteristics of distributions, hypothesis testing and regression analysis, basic concepts and applications of probability theory and statistics, chisquared test.

Recommended Books:

1. Probability and Random Processes: G.R. Grimmett and D.R. Stirzaker
2. Elementary Probability Theory with Stochastic Processes: K.L. Chung

STA 301 Modern Probability Theory & Stochastic Processes 3 Credits

Stochastic Processes: Definition of different types of stochastic processes, recurrent events, renewal equation, delayed recurrent events, number of occurrence of a recurrent event. Markov Chain: Transition matrix, higher transition probabilities, classification of sets and chains, ergodic properties. Finite Markov Chain: General theory of random walk with reflecting barriers, transient states, absorption probabilities, application of recurrence time, gambler's ruin problem. Homogeneous Markov Processes: Poisson process, simple birth process, simple death process, simple birth death process, general birth process, effect of immigration, nonhomogeneous birth death process, Queuing theory. Modern Probability Theory: Probability of a set function, Borel field and extension of probability measure, probability measure notion of random variables, probability space, distribution functions, expectation and moments.

Prerequisite: STA201

Recommended Books:

1. Probability and Random Processes by G.R. Grimmett and D.R. Stirzaker.
2. Elementary Probability Theory with Stochastic Processes by K.L. Chung.
3. The Theory of Stochastic Processes by D.R.Cox and W.Miller
4. Introduction to Probability Models by S.M. Ross.
5. Stochastic Processes by S.Ross
6. Elements of Applied Stochastic Processes by U.N. Bhat.

b. Lab Courses:

MAT 250 Mathematics Lab I 2 Credits

Introduction to the computer algebra package MATHEMATICA/Matlab. Evaluation and graphical representation of function. Solution of linear and nonlinear equations by using False- Position, Bisection, Newton Raphson methods. Solution of system of linear equations by using Gaussian Elimination method. Interpolation and extrapolation. Numerical differentiations. Curve fitting. Trapezoidal and Simpson's rules for numerical integration. Problem solving in concurrent courses (e.g. Calculus, Linear Algebra and Geometry), using FORTRAN, MATHEMATICA and Matlab. Lab Assignments: There shall be at least 15 lab assignments

Recommended Books:

1. FORTRAN Programming: Schaum outline series.
2. Mathematica : Stephen Wolfram.
3. Matlab for engineering applications: W.J. PalmIII.

MAT 350 Mathematics Lab II 2 Credits

Solution of initial value or boundary value problems for Ordinary differential equations. Solution of initial value or boundary value problems for partial differential equations. Problem solving in concurrent courses (e.g; Calculus, Advanced linear algebra problems, Differential Equations and Numerical Analysis, Complex Analysis, Linear Programming, Numerical Analysis and Applied Mathematics) using FORTRAN and MATHEMATICA/Matlab. Lab Assignments: There shall be at least 15 lab assignments.

Recommended Books:

1. FORTRAN Programming: Schaum outline series.
2. Mathematica : Stephen Wolfram.
3. Matlab for engineering applications: W.J. PalmIII.

c. Dissertation:

MAT 400: Project /Thesis 3 Credits

A student is required to carry out project / thesis work in the last two semesters in her/his chosen field. There will be a supervisor who will either be a BRAC University faculty or any other suitable expert from universities and R/D organizations of the country to guide the project / thesis work .On completion of study and research s/he will have to submit the dissertation report and to face a viva board for the defence of the dissertation.

Mathematics Courses for Students of Other Disciplines

Mathematics & Natural Science Department of BRAC University offers the following mathematics courses to undergraduate programmes of Computer Science and Engineering, Computer Science, Electronics and Communication Engineering, Architecture, Bachelor of Business Administration, Economics English and Physics.

MAT 091 Basic Course in Mathematics (Non-credit)

Topics including sets, relations and functions, real and complex numbers system, exponents and radicals, algebraic expressions; quadratic and cubic equations, systems of linear equations, matrices and determinants with simple applications; binomial theorem, sequences, summation of series (arithmetic and geometric), permutations and combinations, elementary trigonometry; trigonometric, exponential and logarithmic functions; coordinate geometry; statics ­ composition and resolution of forces, equilibrium of concurrent forces; dynamics ­ speed and velocity, acceleration, equations of motion.

Recommended Books:

1. Algebra and Trigonometry: Lial and C.D. Miller
2. College Algebra: Michael Sullivan

MAT101 Fundamentals of Mathematics 3 credits

Basic techniques of algebra, Sets and their applications, Polynomials, Inequalities, Linear inequalities , Exponential and Logarithmic functions, Trigonometric Functions, Function , Domain & Range of function, Sketching of functions, Matrix, Properties of Matrix, System of Linear Equations, Matrix solution of system of linear equations, Inverse matrix, determinant, Cramer's rule, Limit and Continuity, Elementary differentiation and application, Integration.

Recommended Books

1. Algebra and Trigonometry (6th edition) : Margaret L.Lial, Charles D. Miller, David I. Scneider.
2. College Algebra (5th edition) : Raymond A. Barnett, Michael R. Ziegler
3. College Algebra(5th edition) : Michael Sullivan

MAT 102 Introduction to Mathematics 3 credits

Factorisation, Synthetic Division, Zeros (Roots) of Polynomials, Relation between Roots and Coefficients, Nature of Roots (Descarte's Rule of signs); Complex Number System, Graphical representation of Complex Numbers (Argand Diagram), Polar form of Complex Numbers; Conic Sections, Parabola, Circle, Ellipse, Hyperbola, Transformation of Coordinates and Applications; Exponential Growth & Decay. Applications; Mathematical Induction; Determinants, Fundamental Properties of Determinants, Minors and Cofactors, Application of Determinants to solve System of Linear Equations (Cramer's, Rule); Introduction to Matrix Algebra, Matrix Multiplication, Augmented Matrix, Adjoint Matrix, Inverse Matrix, Application of Matrices-solution of System of Linear Equations (homogeneous & non-homogeneous), Consistency of System of Equations.

Recommended Books:

1. Algebra and Trigonometry: Lial and C.D. Miller
2. College Algebra: Michael Sullivan

MAT103 Basic Concepts in Mathematics 3 credits

The real numbers, Absolute value of real numbers, Exponents, Polynomials, Basic operations and Factoring of polynomials, Rational expressions, Radicals. Linear Equations, Solutions, graphs and application, Quadratic Equations, Solutions, graphs and applications, Variation, Linear inequalities. Exponential and Logarithmic functions, Exponential growth and decay, Ratios, proportions, percent, application of simple and compound interest. Trigonometric Functions, the sine and cosine functions, Cartesian coordinate systems, Graphing, relations, Equations of a straight line, its slope, Equations of a circle, System of Linear Equations, Matrix. Population, Sample, Variable, Raw data, Frequency distribution table, Graphical presentation, Measures of central tendency and measures of dispersion.

Recommended Books

1. Algebra and Trigonometry (6th edition) - Margaret L.Lial, Charles D. Miller, David I. Scneider.
2. College Algebra (5th edition) - Raymond A. Barnett, Michael R. Ziegler
3. College Algebra(5th edition)­ Michael Sullivan
4. Statistics for management(7th edition)- Richard I. Levin, David S. Rubin

MAT 104 Mathematics 2 credits

Calculus: Function, definition of limit, continuity and differentiability, successive and partial differentiation, maxima and minima, integration, integration by parts, standard integrals, definite integrals.

Solid Geometry: Plane coordinates geometry, System of co-ordinates, Transformation of co-ordinates, projection, Straight lines, Pair of straight lines, Distance between two points, Sphere, Conicoids, Ellipsoid, Paraboloid.

Recommended Books

1. A Text Book on Co-ordinate Geometry and Vector Analysis : Khosh Mohammad(K.M)
2. A Text Book on Co-ordinate Geometry and Vector Analysis : Rahman and Bhattacharjee (R.B)
3. Calculus (7th Edition) : Howard Anton (H.A)
4. Calculus : Thomas and Finney.

MAT 105 Calculus 3 credits

Differential Calculus: Limits, continuity and differentiability, differentiation, Taylor's, Maclaurine's & Euler's theorems, indeterminate forms, tangent and normal, sub tangent and subnormal, maxima and minima, radius of curvature & their applications, introduction to calculus of function of several variables, Taylor's theorem, maxima and minima for function of several variables. Transformation of coordinates & rotation of axes, conic sections.

Integral Calculus: Definition of integration, techniques of integration for definite & indefinite integrals, improper integrals, area, volume and surface integration, arc length and their applications, multiple integrals, Jacobian, line integrals, divergence theorem and Stokes' theorem, beta function and gamma function.

Recommended Books:

1. Calculus: Howard Anton
2. Calculus with analytic Geometry: E. W. Swokowski

MAT 110 Differential Calculus and Coordinate Geometry 3 credits

Differential Calculus: Limits. Continuity and differentiability. Successive differentiation of various types of functions. Liebnitz's Theorem. Rolle's theorem. Mean Value theorem. Taylor's theorem in finite and infinite forms. Maclaurine's theorem in finite and infinite forms. Lagrange's form of remainders. Expansion of functions. Evaluation of indeterminate forms by L'Hospitals rule. Partial differentiation. Euler's theorem. Tangent and normal. Subtangent and subnormal in Cartesian and polar coordinates. Determination of maximum and minimum values of functions and points of inflexion. Application. Curvature. Radius of curvature. Centre of curvature.

Coordinate Geometry: Change of axes. Transformation of coordinates. Simplification of equation of curves. Pair of straight lines. Conditions under which general equations of the second degree may represent a pair of straight lines. Homogeneous equations of the second degree. Angle between the pair of lines. Pair of lines joining the origin to the point of intersection of two given curves. System of circles; orthogonal circles. Radical axes, radical centre, properties of radical axes, coaxial circles and limiting points. Equations of ellipse and hyperbola in Cartesian and polar coordinates. Tangent and normal. Pair of tangent. Chord of contact. Chord in terms of its middle points, parametric coordinates. Diameters. Conjugate diameters and their properties. Director circles and asymptotes. 3 credits. [Students will be expected to attend a 3hour tutorial class, once each week and submit tutorial worksheets.]

Recommended books:

1. A Text Book on Coordinate geometry and Vector Analysis : Kosh Mohammad.
2. The elements of Coordinate geometry : S.L. Loney.
3. Calculus (7th Edition) : Howard Anton.

MAT 120 Mathematics II: Integral Calculus and Differential Equations 3 credits

Integral Calculus: Definitions of integration. Integration by the method of substitution. Integration by parts. Standard integrals. Integration by method of successive reduction. Definite integrals, its properties and use in summing series. Walli's formula. Improper integrals. Beta function and Gamma function. Area under a plane curve in cartesian and polar coordinates. Area of the region enclosed by two curves in cartesian and polar coordinates. Trapezoidal rule. Simpson's rule. Arc lengths of curves in cartesian and polar coordinates, parametric and pedal equations. Intrinsic equations. Volumes of solids of revolution. Volume of hollow solids of revolutions by shell method. Area of surface of revolution.

Ordinary Differential Equations: Degree of order of ordinary differential equations. Formation of differential equations. Solution of first order differential equations by various methods. Solutions of general linear equations of second and higher order with constant coefficients. Solution of homogeneous linear equations. Applications. Solution of differential equations of the higher order when the dependent and independent variables are absent. Solution of differential equations by the method based on the factorization of the operators.
(The course also includes some lab work)

Prerequisites: MAT 110.

Recommended books:

1. Calculus with analytic geometry (7th edition) : Howard Anton
2. A First course in Differential Equations With Modeling Applications (7th edition) : Dennis G. Zill
3. Mathematical Methods : Md. Abdur Rahman.

MAT 203 Matrices, Linear Algebra & Differential Equations 3 credits

Matrices: Types of matrices, algebraic operation on matrices, determinants, adjoint & inverse matrix, orthogonality & diagonalization of matrix.

Linear Algebra: System of linear equations, vector space; 2D-space, 3D-space, Euclidean nD-space, sub space, linear dependence/independence, basis and dimension, row space, column space, rank and nullity, linear transformation, eigen value and eigen vector, matrix diagonalization, application of linear algebra.

Ordinary Differential Equations: Introduction to differential equations, first order differential equations and applications, higher order differential equations and applications, series solutions of linear equations, systems of linear first order differential
equations.

Prerequisite: MAT 105

Recommended Books:

1. Elementary Linear Algebra : Howard Anton
2. Introductory Linear Algebra with Application : Bernard Kolman
3. First Course in Linear Algebra : P.B. Bhattacharya & S.K. Jain
4. A First Course in Differential Equations : D.G. Zill
5. Introduction to Differential Equations : L. Ross

MAT 204 Complex Variables & Fourier Analysis 3 credits

Complex Variables: Complex number systems, general functions of a complex variable, limits and continuity of a function of complex variables and related theorems, complex differentiation and CauchyRiemann equations, mapping by elementary functions, line integral of a complex function. Cauchy's integral theorem, Cauchy's integral formula, Liouville's theorem, Taylor's and Laurent's theorem, singular points, residue, Cauchy's residue theorem, evaluation of residues, contour integration and conformal mapping.

Fourier analysis: Real and complex form, finite Fourier transform, Fourier integrals, Fourier transforms and their use in solving boundary value problems.

Prerequisite: MAT 105

Recommended Books:

1. Complex Variable and Applications: James W Brown and Ruel V Churchill
2. Complex Variables: M R Speigel

MAT 205 Introduction to Numerical Methods 3 credits

Computer arithmetic: floating point representation of numbers, arithmetic operations with normalized floating point numbers; iterative methods, different iterative methods for finding the roots of an equation and implementation of them in computer programmings, solution of simultaneous algebraic equations by various methods, solution of tridiagonal system of equations, interpolation for equispaced and nonequispaced nodes, least square approximation of functions, curve fitting, Taylor series representation, Chebyshev series, numerical differentiation and integration and numerical solution of ordinary differential equations & partial differential equations.

Prerequisite: MAT 203

Recommended Books:

1. Numerical Analysis: R.L. Burden and J.D. Faires
2. Introductory Methods of Numerical Analysis: S.S. Sastry
3. Numerical Recipes: W.H. Press, S.A. Teukolsky, W.T. Vetterling & B.P. Flannery.

MAT 215 Mathematics III: Complex Variables & Laplace Transformations 3 credits

Complex Variables: Complex number systems. General functions of a complex variable. Limits and continuity of a function of complex variables and related theorems. Complex differentiation and CouchyRiemann equations. Mapping by elementary functions. Line integral of a complex function. Cauchy's integral theorem. Cauchy's integral formula. Liouville's theorem. Taylor's and Laurent's theorem. Singular points. Residue. Cauchy's residue theorem. Evaluation of residues. Contour integration. And conformal mapping.

Laplace Transformations: Definition. Laplace transformations of some elementary functions. Sufficient conditions for existence of Laplace transforms. Inverse Laplace transforms. Laplace transforms of derivatives. The unit step function. Periodic function. Some special theorems on Laplace transforms. Partial fractions. Solutions of differential equations by Laplace transforms. Evaluation of improper integrals.

Prerequisites: MAT120.

Recommended books:

1. Complex Variable and Applications; Author: James W Brown and Ruel V. Churchill; 6th Edition
2. Complex Analysis, Cambridge University Press: Stewart and D. Tall.
3. Complex Variables; M R Spiegel; Schuam's Outline Series
4. A First Course in Differential Equations; Author: Dennis G. Zill; 7th Edition
5. Laplace Transform; Author: M R Spiegel; Schuam's Outline Series

MAT 216 Mathematics IV: Linear Algebra & Fourier Analysis 3credits

Matrices: Definition of matrix. Different types of matrices. Algebra of matrices. Adjoint and inverse of a matrix. Elementary transformations of matrices. Rank and Nullity. Normal and canonical forms. Solution of linear equations. Matrix polynomials. Eigenvalues and Eigenvectors. Vectors: Scalars and vectors, equality of vectors. Addition and subtraction of vectors. Multiplication of vectors by scalars. Scalar and vector product of two vectors and their geometrical interpretation. Triple products and multiple products. Linear dependence and independence of vectors. Differentiation and integration of vectors together with elementary applications. Definition of line, surface and volume integrals. Gradient, divergence and curl of point functions. Various formulae. Gauss's theorem, Stroke's theorem, Green's theorem. Fourier Analysis: Real and complex form. Finite transform. Fourier integral. Fourier transforms and their uses in solving boundary value problems.

Prerequisite: MAT 120

Recommended books:

1. Elementary Linear Algebra (8th ed.) by Howard Anton and Chris Rorres.
2. Calculus (7th ed.) by Howard Anton.
3. Introductory linear algebra with applications. (7th ed.) by Bernard Kolman.
4. First course in linera algebra by PB Bhattachary, S K Jain & S R Nagpaul.
5. Mathematical methods Volume2 by Md. Abdur Rahman.

MAT 301 Group Theory 3 Credits

Definition and various examples of groups, subgroups, cosets, normal subgroups, quotient (factor) groups, permutation groups, cyclic groups, generator of a cyclic group, centre of a group, Abelian group, normalizer and centralizer of an element/ subset of a group and its application to physics, group homomorphism, isomorphism and automorphism and related theorems, symmetry groups, SU (3), SU (6), application of group theory in solid state physics & elementary particles.

Recommended Books:

1. Group Theory: Hammermesh
2. Abstract Algebra: P.B Bhattacharya & S.K. Jain & S.R. Nagpaul
3. A First Course in Abstract Algebra: J.B. Fraleigh
4. Modern Algebra: A.K. Agarwal

MAT 303 Tensor Analysis 3Credits

Definition of tensor, tensor density, affine tensor and geometrical object, properties of tensor symmetry, criteria of tensor properties, metric tensor, Kronecker symbol and LeviCivita's symbol, determinant of metric tensor, connection between metric tensor and Dirac's matrices in the Sommerfeld representation, evolution of square root from four dimensional interval in matrix sense, transformation properties of vector partial derivatives by coordinates, connection coefficients and covariant derivatives, Christoffel's symbols, geodetic lines (geodetics) as a generalization of notion of straight line, variation principle for geodetics, parallel transport, connection between geodetics and covariant differentiation, transport along closed line curvature tensor of the 4th rank, curvature tensor of the 2 D rank, scalar curvature, equations of geodetic deviation, curvature expression in terms of Dirac's matrices, Bianchi's identity, Einstein's conservative tensor, integral operations and corresponding theorems.

Recommended Books:

1. Introduction to Tensor Calculus and Continuum Mechanics: J.H.Heinbockel
2. Vector Analysis: Lipschutz, Schaum's Outline Series
3. Tensor Analysis: Md. Abdur Rahaman.