Classroom Teaching
(Last Updated: February 2019)
[6] Ordinary Differential Equations (Spring 2018)
Institution: Heriot-Watt University - Edinburgh, UK
Course code: F19MO
Level: Undergraduate (Mathematics Year 3)
Class size: 150
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Description and Syllabus
This course is an elementary introduction to methods for solving scalar equations and linear systems of ordinary differential equations. The course was based primarily on notes which were provided by the mathematics department at Heriot-Watt. The syllabus was as follows:
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Scalar ODEs
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Systems of ODEs
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Laplace Transforms
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Boundary-Value Problems
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Sturm-Liouville Problems
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Phase Planes
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Sample Course Materials
[5] Ordinary Differential Equations (Spring 2017)
Institution: Heriot-Watt University - Edinburgh, UK
Course code: F19MO
Level: Undergraduate (Mathematics Year 3)
Class size: 150
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Please see above for description and sample materials.
[4] Vector Analysis (Spring 2016)
Institution: New York University - New York City, NY, USA
Course code: MATH-UA 224
Level: Undergraduate (Final Year Mathematics)
Class size: 40
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Course Description and Syllabus
Generally, this course provides a brief review of multivariate calculus: partial derivatives, chain rule, Riemann integral, change of variables, line integrals. Also covered are: Lagrange multipliers, inverse and implicit function theorems and their applications. An introduction to calculus on manifolds is provided with definition and examples of manifolds, tangent vectors and vector fields, differential forms, exterior derivative, line integrals and integration of forms. Gauss' and Stokes' theorems on manifolds are discussed. The general webpage for the course at NYU is available at: https://math.nyu.edu/dynamic/courses/undergrad/math-ua-224/.
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In my iteration, I designed the course supported by James R. Munkres’ textbook, Analysis on Manifolds. The aim of the course was to understand how to generalise the well-known Stokes’ Theorem for surface integrals in R^3 to integrals defined on higher-dimensional subsets of Euclidean space. In order to understand the higher-dimensional analogue of the formula, students studied manifolds, multilinear algebra, differential forms, and integration on manifolds. The rough syllabus reads as follows:
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Topology on N-dimensional Euclidean Space
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Differentiation
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Integration
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Change of Variables
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Multilinear Algebra
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Differential Forms
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Sample Course Materials
[3] Calculus III (Fall 2015)
Institution: New York University - New York City, NY, USA
Course code: MATH-UA 123
Level: Undergraduate (Mathematics/Sciences)
Class size: 50
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Description and Syllabus
Calculus III was a service course run by the Courant Institute of Mathematical Sciences for the benefit of all of New York University’s students. The curriculum for this course was based on the latter chapters of the textbook, Stewart’s Calculus. As was the case for Calculus I, all Instructors for this course could design and distribute notes to their own classes, with the proviso that certain chapters of Stewart’s Calculus be covered. I designed the Midterm examinations for my section of the total cohort (with this cohort being around 400 students in size). As before, the Final exam was centrally-designed, group-checked and also group-marked. The full course description and syllabus can be found at the following official NYU Calculus III webpage: https://math.nyu.edu/dynamic/courses/undergrad/math-ua-123
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Sample Course Materials
[2] Honors Analysis II (Spring 2015)
Institution: New York University - New York City, NY, USA
Course Code: MATH-UA 329
Level: Undergraduate (Final Year Mathematics)
Class size: 13
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Description and Syllabus
This course generally is a continuation of Honors Analysis I, covering topics such as: metric spaces, differentiation of functions of several real variables, the implicit and inverse function theorems, Riemann integral on Rn, Lebesgue measure on Rn, the Lebesgue integral. The general webpage for the course at NYU is available at: https://math.nyu.edu/dynamic/courses/undergrad/math-ua-329/.
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In my iteration, I designed the course supported by 3 textbooks: W. A. Sutherland’s Metric and Topological Spaces, W. Rudin’s Principles of Mathematical Analysis, and T. Tao’s book Analysis II. The rough syllabus reads as follows:
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Basic Metric and Topological Space Theory
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Differentiation in N-dimensional Euclidean Space
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Measure theory in N-dimensional Euclidean Space
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The Lebesgue Integral
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Sample Course Materials
[1] Calculus I (Fall 2014)
Institution: New York University - New York City, NY, USA
Course code: MATH-UA 121
Level: Undergraduate (All)
Class size: 200
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Description and Syllabus
Calculus I was a service course run by the Courant Institute of Mathematical Sciences for the benefit of all of New York University’s students. The curriculum for this course was one which had been developed over a number of years, and it drew particularly strongly from the renowned textbook, Stewart’s Calculus. Nevertheless, all Instructors for this course were afforded freedom to design and distribute notes to their own classes, with the proviso that certain chapters of Stewart’s Calculus be covered therein. I designed the Midterm examinations for my section of the total cohort (the cohort being around 1200 students in size). The Final exam was centrally-designed, group-checked and also group-marked. The full course description and syllabus can be found at the following official NYU Calculus I webpage: https://math.nyu.edu/dynamic/courses/undergrad/math-ua-121/.
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Sample Course Materials
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