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BSMA2001 - Mathematical Thinking
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BSMA2001 - Mathematical Thinking
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| Field | Value |
|---|---|
| Course Code | BSMA2001 |
| Level | Degree Level Course |
| Credits | 4 |
| Type | Elective |
| Pre-requisites | None |
📖 Description
To introduce ideas of proofs and problem solving in mathematics and to help in the transition from learning basic mathematical methods to the learning of more advanced mathematical methods and ideas.
🗓️ Weekly Syllabus
| Week | Topic |
|---|---|
| Week 1 | triangular numbers, Sigma Notation for Summation, Sequences, Peano's axioms for the natural numbers, |
| Set Theory: the language of Mathematics, Hilbert | |
| Week 2 | A Trip to Cantorsville, Cantor's Diagonalization Argument, Towards the Real Numbers, Ordered Field, |
| Completeness Axiom, The Least Upper Bound Property | |
| Week 3 | Currency Game, Divisibility, Greatest Common Divisor, The Euclidean Algorithm, Proof of the Euclidean |
| Algorithm, Test for Divisibility | |
| Week 4 | Fermat's Little Theorem, Fundamental Theorem of Arithmetic, Modular Arithmetic, Arithmetic with |
| Congruences, Infinitude of Primes, Inclusion–Exclusion | |
| Week 5 | Proof of Inclusion-Exclusion Principle, Pigeonhole Principle, Sieve of Eratosthenes, More on the |
| Infinitude of Primes, Gaps Between Primes | |
| Week 6 | Binomial Coefficients, Binomial Theorem, Lattice Paths, Random Sampling, Permutations, Example |
| of Inclusion-Exclusion Principle | |
| Week 7 | Graph Theory - Introduction, Connectedness and Distance in Graphs, Adjacency Matrix, Graph Trees, |
| Sperners Lemma, Graph Coloring | |
| Week 8 | Limit of a Sequence, Properties of Limits, Sequential Continuity, Continuity of Trigonometric |
| functions, Intermediate Value Theorem | |
| Week 9 | Limit of Fibonacci series, Lamé formula, Sandwich Lemma, Shifting Lemma |
| Week 10 | Derivatives, Faà di Bruno's formula |
| Week 11 | Riemann Integrals, Mean Value Theorem |
| Week 12 | Uniform continuity, Fundamental theorem of calculus |
📚 Books & Resources
Prescribed Books
The following are the suggested books for the course:
“Mathematical Thinking: Problem-solving and Proofs”, John D’Angelo and Douglas West, Pearson, 2000 (2nd edition) “Mathematical Proofs: A Transition to Advanced Mathematics”, G. Chartrand, A. D. Polimeni, P. Zhang, Pearson, 2012
📝 About the Instructors
Prof. Amritanshu Prasad
Professor,
The Institute of Mathematical Science,
Chennai
Amritanshu Prasad is a mathematician at The Institute of Mathematical Sciences, Chennai,
...
more
working in algebraic combinatorics and representation theory.
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Prof. Sankaran Viswanath
Professor,
The Institute of Mathematical Science,
Chennai
Sankaran Viswanath is a mathematician at The Institute of Mathematical Sciences, Chennai,
...
more
working in algebraic combinatorics and representation theory.
less