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1. Fall 2016, 4130-Honors Introduction to Analysis 1, Cornell, Teaching Assistant (grader).
2. Spring 2017, 2220-Multivariable Calculus, Cornell, Teaching Assistant (recitations).
3. Fall 2017, 2220-Multivariable Calculus, Cornell, Teaching Assistant (recitations).
4. Spring 2018, 2210-Linear Algebra, Cornell, Teaching Assistant (recitations).
5. Fall 2018, 1120-Calculus 2, Cornell, Instructor.
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6. Spring 2019, 1110-Calculus 1, Cornell, Instructor.
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7. Fall 2019, 1110-Calculus 2, Cornell, Instructor.
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8. Spring 2020, 2220- Multivariable Calculus, Cornell, Teaching assistant (recitations)
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9. Spring 2021, 2 sections of Math 105: Integral Calculus for Commerce and Social Science, UBC, Instructor.
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10. Fall 2021, Math 253: Multivariable Calculus, UBC, Instructor.
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11. Spring 2022, Math 312: Introduction to number theory, UBC, Instructor.
We covered modular arithmetic, the Euclidean algorithm, Fermat’s little theorem, the Legendre symbol, quadratic residues and reciprocity, continued fractions, as well as an introduction to diophantine equations.
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12. Fall 2023, Function field arithmetic, Chennai Mathematical Institute, Instructor.
In this course we study the arithmetic of Drinfeld modules and related structures. These arithmetic objects have properties that are analogous to elliptic curves defined over number fields. The textbook used for this course is "Drinfeld modules" by Papikian.
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13. Fall 2023, Algebraic Geometry I, Chennai Mathematical Institute, Instructor.
I discussed the theory of algebraic varieties and the basics of scheme theory. I covered chapter 1 and most of chapter 2 of Hartshorne’s "Algebraic Geometry".
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14. Fall 2024, Graduate topology I, Chennai Mathematical Institute, Instructor.
This is a core course for graduate students, covering point set topology, as well as some pre- liminaries in algebraic topology. In greater detail, I covered connectedness and compactness, spaces, Tychonoff’s theorem, separation axioms, normal and regular spaces, Urysohn-Tietze theorems, partitions of unity, compactifications. Further, I covered Fundamental groups, covering spaces and the Galois correspondence in this context. Since I had more time to cover additional topics, I introduced the students to the the- ory of vector bundles and topological K theory. The lectures were based on the first 5 chapters in Munkres’ "A first course in topology", the first chapter of Hatcher’s "Algebraic topology" and the first chapter in Hatcher’s "Vector bundles and K theory".
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15. Spring 2025, Arithmetic dynamics, Chennai Mathematical Institute, Instructor.
Throughout, I followed Silverman’s text "Arithmetic of dynamical systems". I was able to cover chapters 1-5 from this textbook. Towards the end
of the course, I discussed some research topics related to Galois theoretic structures which arise in arithmetic dynamics called "arboreal Galois representations", as well as dynamical analogues of various conjectures which have been of interest in arithmetic geometry, like the Manin–Mumford conjecture and Bogomolov conjecture. The material on arboreal Galois representations required some prerequisites from algebraic number theory and infinite Galois theory, which I covered in class. The other topics required more background from arithmetic and diophantine geometry which I covered from Bombieri and Gubler’s text "Heights in diophantine geometry".
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16. Fall 2025, Analytic Number theory, Chennai Mathematical Institute, Instructor.
I followed Overholt’s book "A course in analytic number theory" and I have covered chapters 1, 3, 4 ,5 and 6 namely: arithmetic functions, Dirichlet series, the circle method and the prime number theorem. I also discussed Waring's problem, Hardy-Ramanujan's asymptotic for the partition function, function equations for L-functions and zero free regions for the zeta function, basic theory of diophantine approximation, Roth's theorem, Schmidt's subspace theorem and applications to diophantine equations.