I have taught the following courses at Amherst College:

- Math 111: Introduction to Calculus (Fall 2013, Fall 2012, Fall 2011)
- Math 121: Intermediate Calculus (Spring 2012)
- Math 211: Multivariable Calculus (Spring 2015, Spring 2013, Fall 2012, Fall 2011)
- Math 355: Introduction to Analysis (Spring 2012)
- Math 410: Galois Theory (Fall 2013)
- Math 455: Topology (Spring 2015, Spring 2013)

### Math 111: Introduction to Calculus

This is a one semester introduction to differential and integral calculus. The main topics are:- Limits: limit laws, the ε/δ definition, basic limit calculations
- The derivative: limit definition, geometric meaning, product/quotient/chain rules, implicit differentiation, related rates
- Maximum and minimum problems, optimization
- The Riemann integral, Fundamental Theorem of Calculus

### Math 121: Intermediate Calculus

This is a second-semester calculus course covering:- Integration techniques: integration by parts, trig and hyperbolic substitution, partial fractions
- Improper integrals, L'Hôpital's Rule, calculating volumes
- Sequences and series: convergence, integral test, comparison test, absolute convergence, root and ratio tests, alternating series
- Power series, radius of convergence, Taylor and MacLaurin series
- Parametric curves and arc length, polar coordinates

### Math 211: Multivariable Calculus

This is a standard course of multivariable calculus covering:- Coordinate systems and vectors in two and three dimensions, dot and cross products, equations of lines and planes
- Vector-valued functions, their derivatives and integrals, velocity, acceleration, speed, arc length, curvature
- Functions of several variables, their limits and continuity, partial derivatives, tangent planes, differentiability, directional derivatives, gradient
- Extrema of functions of several variables, second-order partial derivatives, constrained extrema problems, Lagrange multipliers
- Iterated integrals in cartesian, polar, cylindrical and spherical coordinates, changing variables in multiple integrals
- Vector fields, path integrals, Green's Theorem, curl and divergence, Stokes' Theorem

### Math 355: Introduction to Analysis

This is a proof-based course on mathematical analysis and one of the core requirements of the math major at Amherst. It covers:- Completeness of the real numbers, rationals and irrationals, mathematical induction
- Sequences and series: convergence, bounded monotone sequences, Cauchy sequences, Bolzano-Weierstrass Theorem
- Sets of real numbers: countability, open and closed sets, compactness, Heine-Borel Theorem
- Functions and continuity, Intermediate Value Theorem, continuous functions on a compact set, uniform continuity
- Derivatives, Rolle's Theorem and Mean Value Theorem
- Riemann integration
- Uniform convergence of sequences and series of functions, continuity of the limit, derivatives and integrals of series, Weierstrass M-Test, power series

### Math 410: Galois Theory

This is an upper-level elective with Math 350 (Groups, Rings and Fields) as a prerequisite. Galois Theory is the study of the beautiful symmetries that appear in the solutions to polynomial equations. The main topics we cover are:- Polynomials and their roots: the quadratic and cubic formulas, minimal polynomials, symmetric polynomials
- Fields and their extensions: finite and algebraic extensions, splitting fields, algebraic closures, the Fundamental Theorem of Algebra
- Galois extensions: normality and separability, Galois groups, the Galois Correspondence
- Solvable extensions: primitive roots of unity, abelian extensions, insolvability of the general quintic
- Finite fields and their Galois groups
- Constructibility of regular polygons

### Math 455: Topology

This is an upper-level elective with Math 355 (Analysis) as a prerequisite that fulfils the upper-level requirement for honors students in the math major. Topology is the study of 'shape'. More precisely, it is concerned with a notion of shape that is invariant under stretching, squashing and bending, but not under cutting or gluing. From this perspective a circle and a square are essentially the same shape, but a line is different. Many objects, both mathematical and otherwise, have an underlying shape that can be captured through the ideas of topology. The main topics are:- Topological spaces and continuous functions: subspace, quotient and product topologies
- Connectedness and compactness
- Separation axioms and metrizability
- Homotopy and the fundamental group
- Classification of surfaces

I taught the following classes at the University of Georgia:

- Math 2001: Geometry for Elementary School Teachers (formerly Math 5002)
- Math 2002: Algebra for Elementary School Teachers (formerly Math 5003)
- Math 2003: Arithmetic for Elementary School Teachers (also Math 5001)
- Math 4000: Modern Algebra and Geometry I (a first course in abstract algebra)
- Math 5020: Arithmetic for Middle School Teachers
- Math 5030: Geometry for Middle School Teachers
- Math 5035: Algebra for Middle School Teachers
- Math 8200: Algebraic Topology (qualifying exam preparation class for graduate students)

I taught the following classes at Johns Hopkins University:

- Math 106: Calculus I for Biological and Social Sciences
- Math 107: Calculus II for Biological and Social Sciences
- Math 202: Calculus III
- Math 211: Honors Multivariable Calculus
- Math 401: Advanced Algebra I
- Math 402: Advanced Algebra II
- Math 413: Introduction to Topology

I was a TA for the following classes at MIT:

- 18.022: Calculus (Multivariable)
- 18.03: Differential Equations
- 18.821: Project Lab in Mathematics

## Michael Ching

Department of Mathematics

Amherst College

PO Box 5000

Amherst, MA 01002

USA

Telephone: (413) 542-5530

Fax: (413) 542-2550

Email: mching@amherst.edu

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