Minor in Mathematics

Undergraduate students of the university who are not majoring in Mathematics have the option to take a Minor in Mathematics. A Minor in Mathematics can serve two distinct functions (apart from enjoying the beauty of the subject!):

1. Acquiring the academic background for higher studies in mathematics.
2. Acquiring modelling and computational skills for applications of mathematics in other disciplines or in industry.

Academic Requirements:

You have to acquire a minimum of 21 lecture credits from the University Wide Elective (UWE) courses offered by the Department of Mathematics. These 21 lecture credits must satisfy the following:

1. At least 9 lecture credits from Group A: MAT 101 (Calculus I), MAT 260 (Linear Algebra), MAT 280 (Numerical Analysis I), MAT 284 (Probability & Statistics)

2. 3 to 6 lecture credits from Group B: MAT 199, 299, 399, 499 (Projects)

3. Remainder from any other UWEs offered by Department of Mathematics
   
   
4. The above is subject to the further requirement that a course should not count towards both Major and Minor requirements. This may be partially waived for majors which already have a large component of compulsory mathematics courses.

The Undergraduate Advisor for Mathematics will help you work out an appropriate choice of courses depending on your interests and background.

How to Apply and Select Courses:

1. You have to register for the minor – the first step is to obtain permission from the UG Advisor of the Department of Mathematics. The current UG Advisor for Mathematics is Prof. Amber Habib. Start by contacting him during his office hours or send an email to amber.habib@snu.edu.in to make an appointment.
   
   
2. You will select courses for the minor in consultation with the UG Advisor for Mathematics.
   
   
3. You must sign up for the Minor before the end of your 6^th semester. However, it is advisable to do so earlier so that there is sufficient time to plan your courses. The best time is during your 3^rd or 4^th semesters.
   
   
4. Please note that you must register for the minor as described here. It is not enough to merely take adequate credits on your own. 
    
5. If you fail to complete the minor during your first 4 years, you may have to spend an extra semester to complete it. If you do so, any scholarship or fee waiver you were granted for your regular course of study will lapse and you will have to pay the full fees for the extra period.

MAT 110 - Computing

Syllabus for MAT 110 – Computing

This is a compulsory course for BS Mathematics students in their 1^st semester.

Credits (Lec:Tut:Lab)= 1:0:1 (One lecture hour and two lab hours weekly)

Prerequisites: None

Overview: This course provides an introduction to the programs Matlab and Microsoft Excel as tools for mathematical computing. The focus is on their use in applications from the fields of Statistics, Finance, Image Processing etc. Student presentations of assignment solutions will be a major component of the course.

Detailed Syllabus:

1. MATLAB:

• Arithmetic expressions, assignment, input and output, Boolean expressions, conditional statements
• For loop, while loop, nested loops, nested conditionals, vectors, elementary graphics, color schemes in Matlab
• Elementary math functions, Functions with multiple input parameters, plotting
• Two dimensional arrays, sorting, searching, cell arrays, cell arrays of matrices
• Working with image files

2. EXCEL:

• Charts
• Lookup, Match, Index, Offset functions
• Embedding form controls in a spreadsheet
• Array functions, Goal Seek, Solver
• Descriptive statistics with Analysis Toolpak

Main References:

1. Programming in Matlab for Engineers by Stephen J. Chapman, Cengage, 2011.
2. Guide to Matlab by Brian R. Hunt, Cambridge, 2001.
3. Microsoft Excel 2010: Data analysis and Business Modeling by Wayne L. Winston, Prentice Hall India.

Other References:

1. Mastering Matlab 7 by Duane C Hanselman and Bruce L Littlefield, Pearson Education, 2005.
2. Excel 2010 Formulas by John Walkenbach, Wiley India, 2011.
3. Favourite Excel 2010 Tips & Tricks by John Walkenbach, Wiley India, 2011.

MAT 000 - Tutorial

Syllabus for MAT 000 – Tutorial

This is a compulsory course for BS Mathematics students in their 1^st semester.

Credits (Lec:Tut:Lab) = 0:3:0 (3 hours of discussion weekly)

Prerequisites: None

Overview: This course is open only to undergraduates majoring in Mathematics and is a compulsory course during their 1^st semester at SNU. Students will be introduced in a tutorial setting to issues regarding the nature and uses of Mathematics. The intent is to ease the transition from high school to university education, as well as to initiate the student into a more holistic view of Mathematics.

Detailed Syllabus: This course will take up issues such as the concepts of axioms and proof, the role of counter-examples, problem solving techniques, geometric intuition, the process of abstraction, etc. Some time will also be set aside for discussion of topics being studied in other courses.

References:

1. What is Mathematics? by Richard Courant and Herbert Robbins. 2^nd edition, Oxford University Press, 2007
2. How to Solve It by G. Polya. 2^nd edition, Prentice Hall India, 2007
3. The Princeton Companion to Mathematics by T. Gowers, J. Barrow-Green and I. Leader (editors). Princeton University Press, 2008.
4. Mathematical Vistas by Peter Hilton, Derek Holton and Jean Pedersen. Springer International Edition, 2010.

MAT 100 - Precalculus

Syllabus for MAT 100 - Precalculus

This is a compulsory course for BS Mathematics students in their 1^st semester.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: None

Overview: Introduction to modern mathematical language and reasoning: Sets and Functions, Proofs, Number Systems, Limits.

Detailed Syllabus:

1. Sets: Describing sets – roster and set-builder notation, empty set, subsets and equality, power set, finite and infinite sets, the language of logic (and, or, not, quantifiers), union, intersection, complement, Euler and Venn diagrams, algebra of sets, Cartesian product

2. Relations and Functions: Relations, functions, real functions and their graphs, increasing & decreasing functions, transformations of functions and their graphs, algebra of functions, composition, one-one functions, onto functions, inverse of a function

3. Number Systems: Review of N, Z and Q, mathematical induction, sup and inf, order completeness of R, Archimedean property of R, applications of completeness (existence of square roots, real powers), C.

4. Catalog of Real Functions: Polynomial functions and graphs, division of polynomials, factor theorem, rational functions, exponential functions, logarithmic functions, trigonometric functions, trigonometric graphs

5. Limits: Estimating limits numerically, examples of existence and non-existence, limit laws, applications of limit laws, one-sided limits, tangent lines and derivatives, limits at infinity, limits of sequences

References:

1. Precalculus by James Stewart, Lothar Redlin and Saleem Watson. Cengage. 5^th ed.
2. Understanding Mathematics by K B Sinha et al, Universities Press.

MAT 101 - Calculus I

Syllabus for MAT 101 – Calculus I

This is a compulsory course for B.Tech. students in their 1^st semester.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: Class XII mathematics or MAT 100 (Precalculus)

Brief Description:

This course covers one variable calculus and applications. It forms the base for subsequent courses in advanced vector calculus and real analysis as well as for applications in probability, differential equations, optimization, etc.

Detailed Syllabus:

1. Differentiation: Functions, limits, sandwich theorem, continuity, intermediate value theorem, tangent line, rates of change, derivative as function, algebra of derivatives, implicit differentiation, related rates, linear approximation, differentiation of inverse functions, derivatives of standard functions (polynomials, rational functions, trigonometric and inverse trigonometric functions, hyperbolic and inverse hyperbolic functions).
2. Applications of Differentiation: Indeterminate forms and L'Hopital's rule, absolute and local extrema, first derivative test, Rolle's theorem, mean value theorem, concavity, 2^nd derivative test, curve sketching.
3. Integration: Area under a curve, Riemann sums, integrability, fundamental theorem, mean value theorem for integrals, substitution, integration by parts, trigonometric integrals, partial fractions, improper integrals.
4. Applications of Integration: Area between curves, volume, arc length, applications to physics (work, center of mass).
5. Ordinary Differential Equations: 1^st order and separable, logistic growth, 1^st order and linear, 2^nd order linear with constant coefficients, method of undetermined coefficients, method of variation of parameters.

Main References:

• Essential Calculus – Early Transcendentals, by James Stewart. Cengage, India Edition.
• Advanced Engineering Mathematics, Erwin Kreyszig, 9^th edition, Wiley India, 2011.

Supplementary References:

• Advanced Engineering Mathematics, Dennis G Zill and Warren S Wright, 4^th edition, Jones and Bartlett.
• The Calculus Lifesaver, by A Banner, Princeton, 2007.
• Calculus and Analytic Geometry by G B Thomas and R L Finney, 9^th edition, Pearson.

MAT 102 - Calculus II

Syllabus for MAT 102 – Calculus II

This is a compulsory course for BS Mathematics students in their 3^rd semester.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: MAT 101 (Calculus I) or equivalent

Brief Description: The first part deals with series of numbers and functions. The second part is an introduction to multivariable calculus, finishing with the various versions of Stokes' theorem. The concepts and techniques covered here are used extensively in the social and natural sciences as well as in engineering to study systems with many dimensions.

Detailed Syllabus:

1. Sequences and Series: Limits of sequences, algebra of limits, series, divergence test, comparison and limit comparison tests, integral test, alternating series test, absolute convergence, root & ratio tests, power series, Taylor series

2. Vectors: Dot and cross product, equations of lines and planes, quadric surfaces, space curves, arc length and curvature

3. Differential calculus in several variables: Functions of several variables, level curves and surfaces, limits and continuity, partial derivatives, tangent planes, chain rule, directional derivatives, gradient, Lagrange multipliers, extreme values and saddle points, 2^nd derivative test

4. Double and triple integrals: Double integrals over rectangles, double integrals over general regions, double integrals in polar coordinates, center of mass, triple integrals, triple integrals in cylindrical coordinates, triple integrals in spherical coordinates, change of variables

5. Vector Integration: Vector fields, line integrals, fundamental theorem, independence of path, Green's theorem, divergence, curl, parametric surfaces, area of a parametric surface, surface integrals, Stokes' theorem, Gauss' divergence theorem

Main Reference:

• Essential Calculus – Early Transcendentals, by James Stewart. Cengage, India Edition.

Supplementary References:

• Calculus and Analytic Geometry by G B Thomas and R L Finney, 9^th edition, Pearson.
• Basic Multivariable Calculus by J E Marsden, A J Tromba and A Weinstein, 1^st edition, Springer (India), 2011.
• Calculus by Ken Binmore and Joan Davies, 1^st edition, Cambridge, 2010.

MAT 240 - Algebra I

Syllabus for MAT 240 – Algebra I

This is a compulsory course for BS Mathematics students in their 3^rd semester.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Overview: Learning traditional Abstract Algebra in a contemporary style. The course will cover the standard algebraic structures of groups, rings and fields up to the Fundamental Theorem of Algebra.

Detailed Syllabus:

Module I: Groups

1. Definition and examples, abelian and non-abelian groups, finite and infinite groups
2. Subgroups: characterisations, subgroup generated by a subset, commutator subgroup, center
3. Cyclic Groups: Properties, classification of subgroups
4. Permutation Groups: definition and notation, examples, properties, Symmetric group on n letters (S_n), Alternating group (A_n) on n letters
5. Cosets and Lagrange's theorem
6. External Direct Product: Definition and examples, properties, criteria for external direct product to be cyclic, finitely generated abelian groups

Module II: Morphisms

7. Normal subgroups, factor groups, internal direct products
8. Group homomorphism: Definition and examples, properties
9. Isomorphism, First Isomorphism Theorem, automorphism, properties, examples

Module III: Rings

10. Introduction to Rings: Definition, examples, properties
11. Subrings
12. Ideals, factor rings, prime ideals and maximal ideals
13. Polynomial Rings: Notation and terminology, division algorithm

Module IV: Extension Fields

10. Integral Domain, definitions and examples, Fields, Characteristic
11. Examples of Fields, algebraic and transcendental elements, degree of a field extension
12. Finite Fields: examples, Fundamental Theorem of Algebra

Main Reference:

• Contemporary Abstract Algebra by Joseph A. Gallian, 4^th edition. Narosa, 1999.

Other References:

• Topics in Algebra by I.N. Herstein, 2^nd Edition. Wiley India, 2006.
• Algebra by Michael Artin, 2^nd Edition. Prentice Hall India, 2011.
• A First Course in Abstract Algebra by John B. Fraleigh, 7^th Edition. Pearson, 2003.
• Undergraduate Algebra by Serge Lang, 2^nd Edition. Springer India, 2009.

MAT 210 Programming

Syllabus for MAT 210 – Programming

This is a compulsory course for BS Mathematics students in their 3^rd semester.

From XKCD. Thanks to Aman Agarwal for the reference!

Credits (Lec:Tut:Lab)= 1:0:1 (One lecture hour and three lab hours weekly)

Prerequisites: None

Overview: This course provides an introduction to formal programming languages via the medium of Python 3.0. The programming activities will be centered around mathematical models involving differential equations, algebraic systems, iterative processes, linear transformations, random processes etc. The course begins with Python language constructs and moves to an in-depth exploration of the SCIPY and NUMPY packages that hold the key to the desired mathematical simulations.

Detailed Syllabus:

1. Basics of the PYTHON programming language:

• Input and output statements, formatting output, copy and assignment, arithmetic operations, string operations, lists and tuples, control statements
• User defined functions, call by reference, variable number of arguments
• One dimensional arrays, two dimensional arrays, random number generation
• Classes, static data, private data, inheritance, scope of variables, nested functions

2. The NUMPY and SCIPY packages:

• Numpy numerical types, data type objects, character codes, dtype constructors.
• Mathematical libraries, plotting 2D and 3D functions, ODE integrators, charts and histograms, image processing functions.
• File I/O, loading data from CSV files
• Using SCIPY/NUMPY to solve models involving difference equations, differential equations, finding limit at a point, approximation using Taylor series, interpolation, definite integrals.

Main References:

1. John Zelle, Python Programming: An Introduction to Computer Science. Franklin, Beedle & Associates Inc., Second Edition, 2010.
2. Ivan Idris, Numpy 1.5 Beginner’s Guide. Packt Publishing, 2011.
3. Hans Petter Langtangen, A Primer on Scientific Programming on Python. Springer, Second Edition, 2011.

Other References:

1. Hans Petter Langtangen, Python Scripting for Computational Science. Springer, 2010.
2. David M. Beazley, Python Essential Reference, 3^rd Edition. Pearson, 2009.
   
   

MAT 202 - Mathematical Methods

Syllabus for MAT 202 – Mathematical Methods

This is a compulsory course for B.Tech students in their 3rd semester.
 
Credits (Lec:Tut:Lab)= 3:0:0 (3 lectures weekly)

Prerequisites: Class XII mathematics

Brief Description: The first part is an introduction to multivariable calculus, finishing with the various versions of Stokes' theorem. The second part deals with series of numbers and functions (such as power series and Fourier series) and their applications to solving differential equations. The concepts and techniques covered here are used extensively in the social and natural sciences as well as in engineering to study systems with many dimensions.

Detailed Syllabus:

1. Computer Algebra System (CAS): Equations, solving linear system, function definition, function evaluation, two and three dimensional plots, differentiation, integration, matrices, matrix algebra, simplification of expressions

2. Differential calculus in several variables: Space curves and arc length, functions of several variables, level curves and surfaces, limits and continuity, partial derivatives, tangent planes, chain rule, directional derivatives, gradient, Lagrange multipliers, extreme values and saddle points, 2^nd derivative test

3. Double and triple integrals: Double integrals over rectangles, double integrals over general regions, double integrals in polar coordinates, center of mass, triple integrals, triple integrals in cylindrical coordinates, triple integrals in spherical coordinates, change of variables

4. Vector Integration: Vector fields, line integrals, fundamental theorem, independence of path, Green's theorem, divergence, curl, parametric surfaces, area of a parametric surface, surface integrals, Stokes' theorem, Gauss' divergence theorem.

5. Series and Applications: Limits of sequences, algebra of limits, series, divergence test, comparison and limit comparison tests, integral test, alternating series test, absolute convergence, root & ratio tests, power series, Taylor polynomials and series, power series method for solving ODEs, Legendre's equation, Bessel's equation, orthogonal functions and Sturm-Liouville problem, periodic functions and trigonometric series, Fourier series, half-range expansions, Fourier integral, heat equation

Main References:

• Essential Calculus – Early Transcendentals, by James Stewart. Cengage, India Edition. (Chapters 8 to 13)
• Advanced Engineering Mathematics, Erwin Kreyszig, 9^th edition, Wiley India, 2011.

Supplementary References:

• Advanced Engineering Mathematics, Dennis Zill and Warren Wright, 4^th ed., Jones & Bartlett, 2011.
• Calculus and Analytic Geometry by G B Thomas and R L Finney, 9^th edition, Pearson.
• Basic Multivariable Calculus by J E Marsden, A J Tromba and A Weinstein, 1^st edition, Springer (India), 2011.

Journals for Students

The SNU library now offers online access to many maths journals from the campus. The main repositories are JSTOR and SpringerLink. Some are particularly good for students:

American Mathematical Monthly "Publishes articles, as well as notes and other features, about mathematics and the profession. Its readers span a broad spectrum of mathematical interests, and include professional mathematicians as well as students of mathematics at all collegiate levels."


College Mathematics Journal "Emphasizes the first two years of the college curriculum. The journal contains a wealth of material for teachers and students."

Mathematical Gazette "The original journal of the Mathematical Association and it is now over a century old. Its readership is a mixture of school teachers, college and university lecturers, educationalists and others with an interest in mathematics" 

Mathematical Intelligencer "Not only does The Mathematical Intelligencer inform a broad audience of mathematicians and the wider intellectual community, it also entertains. Throughout, the journal, humor, puzzles, poetry, fiction, and art can be found. The journal also features information on emergent mathematical communities around the world, new interdisciplinary trends, and relations between mathematics and other areas of culture."

Once on campus, you should be able to access all of these!

CCC 801 - Art of Numbers

Syllabus for CCC 801 – Art of Numbers

Credits (Lec:Tut:Lab) = 1.5:0:0 (3 lectures weekly over a half-semester)

Overview: This course deals with two aspects of numbers. In the first part of the course we will take up some unexplored patterns that exist in nature, study them and understand some of their applications. The second part looks at numbers as carriers of information about our lives. Here we learn how to analyze and present data in ways that help us make sense of our lives. We'll use the spreadsheet program in Open Office to analyze the data in depth.

Detailed Syllabus:

Part A: Fun with Numbers

1. Moessner’s Magic
2. Permutation, Combinations
3. Pascal Triangle, Binomial Theorem
4. Fibonacci Sequence
5. Some applications

Part B: Handling Data

6. Interacting with real time data
7. Descriptive Statistics like mean, median, mode, range, standard deviation, percentiles, quartiles
8. Introduction to a Spreadsheet program (Open Office or Excel)
9. Charts – Bar Charts, Histograms, Line Charts, Pie Charts
10. Simulations
11. Case Studies

Assessment:

Assignments	20%
Presentations	40%
Term Paper	40%

References:

1. The Book of Numbers by John Horton Conway, Richard K. Guy. 2^nd edition, Copernicus.
2. The Heart of Mathematics: An Invitation to Effective Thinking by Edward B. Burger, Michael Starbird. 3^rd edition, Wiley.
3. The Visual Display Of Quantitative Information by Edward Tufte. 2^nd edition, Graphics Press.
4. Excel 2007 for Starters: The Missing Manual by Matthew MacDonald. Shroff/O'Reilly.
5. Analyzing Business Data with Excel by Gerald Knight. Shroff/O'Reilly.

CCC 101 - Mathematics in India

Syllabus for CCC 101 – Mathematics in India

Credits (Lec:Tut:Lab) = 1.5:0:0 (3 lectures weekly over a half-semester)

Prerequisites: None

Overview: Mathematics had a rich history in ancient and medieval India. Indian mathematicians made original contributions to algebra, number theory and geometry; while the Kerala school made fundamental discoveries related to differential calculus and infinite series two centuries before their full development by Newton and Leibniz. This course will provide an overview of the story of mathematics in India, and also incorporate the social context and the connections with other civilizations.

Detailed Syllabus: Issues of dating, translation and interpretation; prehistory; the ancient civilizations of Egypt, Iraq, China and America; Indus Valley Civilization; Mathematics in the Vedas and Puranas; Pythagoras theorem; Applications to grammar, logic, astronomy and technology; Medieval mathematicians and schools of mathematics; Universities; Invention of Zero; Trigonometry; Rates of change; π; Connections with Greece, China and the Arabs; The Kerala school.

Assessment:

Assignments	20%
Class Performance	10%
Term Paper	40%
Presentation	30%

References:

1. Mathematics in India by Kim Plofker, Princeton University Press.
2. Studies in the History of Indian Mathematics by C S Seshadri (ed.), Hindustan Book Agency.
3. Contributions to the History of Indian Mathematics by Gerard G Emch et al (ed.), Hindustan Book Agency.
4. History of Mathematics by Carl B Boyer and Uta C Merzbach, Wiley.