Mathematics

The outcome of a Mathematics Undergraduate Degree, first and foremost, is to develop a mathematical way of thinking. This way of thinking requires unsparing doubt and therefore the standards of rigour are tied to the concept of the proof. Our Mathematics curriculum is designed to initiate students to proof first through the first year core course on Mathematical Reasoning where they learn logic, combinatorial methods of counting and become cognisant of the notion of a function, and second through the unique course on Proofs and Ideas which, while reinforcing their learnings, introduces them to foundational techniques and strategies of proof. This course is also the student’s first encounter with the writing of proof. 
We think by writing and the skills of writing proofs that students learn here become their tools that they hone, refine, sharpen as they learn more and more strategies in different mathematical contexts.

Our curriculum is focused on laying a very strong foundation in modern mathematics for our students. This means that we are uncompromising in our commitment to two course sequences – one on Analysis and another on Algebra. While Analysis is the formalisation of calculus, Algebra does the same for manipulation of symbols, equations, symmetries. Our students come away developing ease with the calculations of limits of sequences, series and functions, differentiation of functions of one and multiple variables, as well as integration in one and many dimensions and on curves and surfaces. These calculations are given a theoretical grounding through the formal aspects of analysis in the form of the so-called epsilon-delta formalism which only takes on more complex facets as students grow in their mathematical maturity. Similarly, with Algebra, as they develop facilities with calculations of solutions of systems of equations, eigenvalues, eigenvectors, calculations related to symmetries, the students become trained in the thought process and proof techniques specific to the study of algebra. This is supplemented by a grounding in Topology and Geometry.

Mathematical culture has taught us the value of rigour as we have seen many a delicate argument fall apart under scrutiny. This utmost attention to detail and nitpicking is a habit that students are made to develop and encouraged into. It is no surprise then that our students are always ready to challenge weak arguments. Our teaching methods reflect this as we do not offer up either theorems or proofs on a platter but engage students in a discourse on developing them with our guidance. This makes the critical thinking skills of Mathematics unmatched in other disciplines.

This requirement of critical thinking is the reason behind our (and every good Mathematics curriculum’s) unrelenting insistence on proof as the vehicle of not just mathematical understanding but also the fun inherent in the challenge of a theorem. This rigor is also transferred to our Applied Mathematics courses on Differential Equations, Numerical Methods, Probability and Statistics. We would be remiss if we did not hold application based courses to the same level of scrutiny and critical thought as we did our core and foundational courses. Therefore, these courses lean heavily on the single and multivariable calculus and linear algebra courses to develop their arguments. Yes, the students learn to solve differential equations by hand and on computer, yes, they learn how to solve systems of linear equations by hand and on a computer, but they also learn why those algorithms work and the proofs are always joyous. They also develop programming skills in Python, Julia and R in the courses as they implement algorithms from numerical methods on the computer. In a world where machines are being imposed on us to do our thinking, we are making sure that our students do not outsource their thinking to machines.

Finally, about electives, apart from the standard electives on Number Theory, Combinatorics, Graph Theory, Measure Theory which are all important either from the point of view of mathematical culture or their intersections with other disciplines, there is also an elective on writing in Mathematics and Scientific Journalism where the students learn the skills of writing technical as well as journalistic articles.