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Mathematics

The study of mathematics is both beautiful and highly applicable, it is both a language on its own and language of the sciences. Study of mathematics enables students to take up a variety of careers ranging from academic research, education, development and quantitative applications in industry.

Students are often motivated by the beauty, rigour, abstractness and applicability of mathematics. Our mathematics curriculum aspires to cater to diversity of students, no matter what their motivation to learn mathematics. Students will get to explore mathematics in various interdisciplinary contexts and with interdisciplinary faculty. They will also gain from intense interaction and mentoring from faculty.

The teaching approach followed in the major is informed by the very way mathematical knowledge is built. A mathematician observes, notices patterns, asks questions, makes guesses, makes hypothesis and then tries to prove the claim through deductive reasoning. Our goal is to help students understand the practice of mathematics and master core foundational aspects of mathematics.

COURSES

The Mathematics major is split into two sections- The first section is the disciplinary part which has core courses (8) and electives (3). The pedagogical approach (Inquiry Based Learning) in the first- year courses gives importance to the journey of mathematical exploration.

Core Courses (24 credits)(Click to expand)

  • Introduction to mathematical thinking 1
  • Introduction to mathematical thinking 2
  • Calculus 1

The second- and third-year courses use a mix of Inquiry Based Learning (IBL) and traditional lecture-tutorial method and will expose students to higher order mathematical concepts.

  • Linear Algebra
  • Abstract Algebra
  • Probability
  • Calculus 2
  • Calculus 3

Elective Courses (9 credits)(Click to expand)

In addition, students will choose elective courses (9 credits) which are designed to cater to the interest of student in the direction of

  • Data- Computing
  • Economics
  • Physics
  • Pure Mathematics

(Please note that course offerings will vary from year to year and will have specific entry criteria for enrollment)

Supporting Courses (15 credits)(Click to expand)

Supporting courses (15 credits) give a broad overview of applications of mathematics in related disciplines. These could include courses in introductory physics, chemistry, biology and economics. In addition, students will complete a two- semester sequence in programming which will develop skills in numerical methods, simulations and functional programming.

Honours

The honours pathway is designed to intensify the exploration of Mathematics and ignite a spark in the mind of the student.

Honours students have to complete additional 12 credits and the pathway has three parts :

  • Research methods course (3 credits),
  • Two electives (6 credits) and
  • An independent study project (3 credits).

The research methods course will expose the student to a variety of topics across various branches and exposure to the research being done in these areas. Experts in subject areas will be invited to interact with students and discuss their work. The two electives will give them further in-depth exposure to advanced topics. Finally, the independent study project done over the breaks after fourth and fifth semester will culminate in sixth semester with a thesis that is written and presented in the sixth semester.

Faculty Speak


Click here to listen to our faculty Shantha Bhushan.



She explains how important it is for students to see the applicability in different areas. Connection of Mathematics not only limited to Engineering or Physics, but also the applicability of Mathematics in Art is important.

COURSE DETAILS(Click to expand)

Brief description of the courses offered in Mathematics major are given below

Introduction to mathematical thinking 1

  • Overview of the scope of mathematics, its subfields and applications
  • Review of functions, graphs and trigonometry
  • Propositional logic
  • Set theory
  • Writing mathematical proofs
  • Number systems and elementary number theory

Introduction to mathematical thinking 2

Selected introductory topics in

  • Plane geometry
  • Combinatorics
  • Graph theory

Calculus with Analytic Geometry 1

  • Tangents and limits
  • Differential calculus and applications
  • Introductory differential equations
  • Introductory integral calculus

Linear Algebra

  • Matrices, Matrix operations, linear independence
  • Bases, dimensions, and vector spaces
  • Eigenvalues, eigenvalue problems
  • Similarity transformations and diagonalization

Abstract Algebra

  • Equivalence relations
  • Groups, Rings and homomorphisms
  • Symmetries
  • Polynomials and their generalizations

Probability

  • Discrete and combinatorial probability, Bayes theorem and discrete distributions
  • Continuous probability, moments and moments generating functions
  • Continuous distributions and the central limit theorem
  • Probability in two variables, joint distributions

Calculus 2 (Analysis, Analytic Geometry )

  • Integral calculus, volumes and areas
  • Sequences, series and convergence
  • Conic sections, polar coordinates

Calculus 3 (Multivariable calculus)

  • Vectors and vector valued functions
  • Curvature, tangential and normal components
  • Lines, planes and quadratic surfaces
  • Functions of several variables, directional derivatives, extreme value problems
  • Multiple integrals
  • Line integrals, conservative fields, Stoke's and Green's theorems
  • Inverse and implicit function theorems


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