Quantitative Reasoning and Mathematical Thinking

Code: FC-0306-1 | Semester: Monsoon 2026

FC Section: First Year

Mathematics is a fundamental part of human culture, dealing with truth and beauty. It can be viewed as a world governed by logic and reason, which we discover using our intuition and creativity. It is also an indispensable tool for all other sciences and thereby essential to understanding the world we live in.

This course will introduce some of the simplest and most basic mathematical ideas. These include sets and mappings, logic and reasoning, graphs and networks, groups and symmetries, modular arithmetic, discrete probability, and a bit of statistics.

Every concept will be illustrated with numerous examples. Emphasis will be placed on precision and clarity. Students are expected to imbibe the idea of a mathematical proof and to apply their knowledge to concrete problems.

Code: FC-0306-2 | Semester: Monsoon 2026

FC Section: First Year

The course will begin with pre-requisite tools of quantitative thinking vis-a-vis the number system, set theory, logic, proofs, probability and statistics. We will then learn how to use some of these tools to study (i) fairness in division of scarce resources, (ii) collective decisions in committees and democracies around the world (voting methods), and (iii) how to act optimally in competitive social interactions, i.e. game theory. By the end of the course, students would have a basic understanding of the most widely used mathematical tools in the liberal arts. They will learn how to approach different economic problems by reducing them to their bare essentials (via modelling) and to mathematically analyse their underlying structural and logical patterns.

Code: FC-0306-3 | Semester: Monsoon 2026

FC Section: First Year

Mathematical ideas, often based on data and analysis, play a key role in understanding the world around us and in making rational decisions.  This course will focus on consequential real-world problems and discuss the underlying mathematical ideas that illuminate the problem structure and help us make more informed and better decisions.

The questions we consider include the ones that rely on taming uncertainty, such as

• What do income inequality, damage from earthquakes and size of cities have in common?
• How to estimate and manage supplies at an Ashoka Coffee shop
• How do fashion stores decide how many clothes to order in a business cycle
• How tools such as the Monte Carlo method help us measure and control disease spread
• How to make profitable investments in stock markets
• The underlying mathematical principles in pricing financial derivative securities

As well as those that involve problems under certainty assumptions, such as

• How do utility companies decide how much electricity to generate from various power sources (coal, natural gas, nuclear, solar, wind) hour by hour?
• How to estimate the price of a home from data such as square footage, number of bedrooms, location rating, age of the property, and local crime rates.
• How do banks feed historical customer data (income, debt, repayment history) into machine learning models to evaluate a new applicant’s risk level and automatically approve or deny lines of credit
• How can individual rational decisions lead to a collectively terrible outcome?
• Can a group of men and women be matched in a stable manner so that there is no pair of individuals who would both prefer to leave their assigned partners to be with each other.
• How Google finds the shortest path from your hometown to Ashoka University

Along the way, students will encounter introductory ideas from probability, statistics, optimisation, regression, machine learning, game theory, matching theory, and graph algorithms.  By the end of the course, students will be able to recognise mathematical structure in unfamiliar situations and reason carefully with data and uncertainty. The broader aim is to develop a form of intellectual independence: the ability to look beneath the surface of a problem and identify its underlying structure.

Code: FC-0306-4 | Semester: Monsoon 2026

FC Section: First Year

This course will introduce students to the basics of mathematical and logical reasoning, algorithmic thinking, and data-driven analysis. The course will use examples from diverse fields to highlight the importance of these in a problem-solving approach. The course will have a strong emphasis on computational thinking.

Please see the course web page for an overview of the coverage.

Code: FC-0306-5 | Semester: Monsoon 2026

FC Section: Senior Year

This is a course about how mathematicians think, taught entirely through puzzles. Each topic opens with a puzzle, a question that is easy to state and tempting to play with, but whose resolution requires a genuine idea, and introduces interesting mathematics.

The students will be active participants rather than passive consumers of a typical “fact of the matter” style of information avalanche.

The course assumes no mathematics beyond basic high school arithmetic.

We do not assume any fondness for mathematics.

On the contrary, the course is designed for those who have so far found mathematics dry, intimidating, or pointless, and aims to change that student’s mind.

Following is a rough course outline.

• Knights. Chess puzzles in which knights jump around on a small board.
• Logical thinking. Card-flipping tests, prisoners guessing their own hat colours, and islands of truth-tellers and liars teach us what it really means to test a claim of the form “if this, then that,” and how much we can deduce from what others do and do not say.
• Machines with finite memory. We build imaginary machines that read a string of symbols and decide whether to accept it. We learn to reverse- engineer such a machine from its wiring, to combine machines with AND, OR, and NOT, and discuss the machines’ limitations.
• The algebra of yes and no. With only two values and two operations, we build a miniature arithmetic in which logical conditions become equations one can actually solve. The liar-and-truth-teller puzzles, attacked earlier by hand, now become a matter of calculation.
• Circuits. The same two-value algebra is wired using physical gates. This is the design principle behind every digital chip.
• Infinity. A frog hops along an endless row of lily pads, and a hunter must guarantee a hit.  
• Permutatonis. We study the act of rearranging things: shuffles of a row of objects, how every shuffle breaks into independent cycles. With it we settle the famous Fifteen Puzzle.

A word on what this course is, and is not, about. It is about reasoning, and doing that reasoning properly.

It is not about symbols. The reader will almost never be asked to write down a formula or manipulate the dense notation that mathematics is often, wrongly, identified with.

Where a symbol does appear, it is only a convenient shorthand for something already stated in plain words, and never a prerequisite for following along.

Code: FC-0306-7  | Semester: Monsoon 2026

FC Section: Senior Year

This foundation course will involve learning some ideas in Mathematics.  You will learn many concepts that occur in mathematics and how they play a role in problem-solving in various disciplines.