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 2013, Fall 2012, Fall 2011)
- Math 355: Introduction to Analysis (Spring 2012)
- Math 410: Galois Theory (Fall 2013)
- Math 455: Topology (Spring 2013)

Here are some descriptions and links for the classes I taught 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)

### Math 2001: Geometry for Elementary School Teachers

*Note that this class has previously been taught as Math 5002.*

This class is intended for students interested in the Early Childhood Education program at the University of Georgia. It covers the basic geometry that elementary school teachers need to know, including:

- angles, parallel lines, triangles, quadrilaterals and circles
- what it means to 'measure' something
- why the standard formulas for area work (for areas of rectangles, triangles and paralellograms)
- why the formulas for volume work (for volume of boxes, prisms and pyramids)

**strongly**recommended that future elementary teachers take the sequence 2001/2/3. These classes satisfy your core math requirements and will be much more use to you as a teacher than precalculus.

The focus for this class is to help students explain *why* standard formulas and methods work so that math is not just viewed as a set of rules without meaning behind them.

The usual textbook for the class is: *Mathematics for Elementary Teachers*, by Sybilla Beckmann.

### Math 2002: Algebra for Elementary School Teachers

*Note that this class has previously been taught as Math 5003.*

This class is intended for students interested in the Early Childhood Education program at the University of Georgia. It covers the basic algebra that elementary school teachers need to know. Topics include:

- Ratios and proportion
- Expressions, formulas and equations, and where they come from
- Functions and their graphs, linear functions
- Prime numbers, factors, multiples, divisibility

The textbook for this class is the same as for Math 2001: *Mathematics for Elementary Teachers*, by Sybilla Beckmann.

### Math 2003: Arithmetic for Elementary School Teachers

*Note that this class is also taught as Math 5001 for students that transfer into the Early Childhood Program..*

This class is intended for students interested in the Early Childhood Education program at the University of Georgia. It covers the basic arithmetic that elementary school teachers need to know. Topics include:

- Decimal notation, comparing decimals, rounding
- The meaning of fractions, equivalent fractions, common denominators, percent
- Addition and subtraction of whole numbers and fractions; why the standard algorithms work
- The meaning of multiplication, commutative, associative and distributive properties, why the standard algorithm works
- Multiplying fractions, understanding story problems for fractions
- The two meanings of division

The textbook for this class is the same as for Math 2001 and 2002: *Mathematics for Elementary Teachers*, by Sybilla Beckmann.

### Math 4000: Modern Algebra and Geometry I

This is a first class in abstract algebra, covering the following topics:

- Integers, divisibility, Euclidean algorithm, modular arithmetic
- Rings, zerodivisors, domains
- Rational, real and complex numbers
- Polynomials, Euclidean algorithm, fundamental theorem of algebra
- Ring homomorphisms, quotient rings, isomorphism theorem

The textbook usually used is: *Abstract Algebra: A Geometric Approach*, by Ted Shifrin, Prentice Hall, 1996. We cover approximately chapters 1-4.

Here is a more detailed list of topics covered in the class.

### Math 5020: Arithmetic for Middle School Teachers

This class is intended for students in the Middle School Education program at the University of Georgia that have chosen Mathematics as one of their areas of specialization. It covers the basic arithmetic that middle school teachers need to know. The content for this class is similar to that for Math 2003, above, except that some sections are skipped in order to go deeper into certain topics. The textbook is the same as for Math 2003.

### Math 5030: Geometry for Middle School Teachers

This class is intended for students in the Middle School Education program at the University of Georgia that have chosen Mathematics as one of their areas of specialization. It covers the basic geometry that middle school teachers need to know. The content for this class is similar to that for Math 2001, above, except that some sections are skipped in order to go deeper into certain topics. The textbook is the same as for Math 2001.

### Math 5035: Algebra for Middle School Teachers

This class is intended for students in the Middle School Education program at the University of Georgia that have chosen Mathematics as one of their areas of specialization. It covers the basic arithmetic that middle school teachers need to know. The content for this class is similar to that for Math 2002, above, except that some sections are skipped in order to go deeper into certain topics. The textbook is the same as for Math 2002.

### Math 8200: Algebraic Topology

This is a first class in algebraic topology at the graduate level. It is intended to prepare students in the UGA Math Department Ph.D. program for the algebraic topology portion of their written qualifying exam in topology. Topics covered include:

- homotopies between maps and homotopy equivalences, deformation retractions
- fundamental group and van Kampen's Theorem
- simplicial homology, basic calculations
- singular homology, relative homology, excision, the Mayer-Vietoris sequence
- the degree of a self-map of a sphere
- CW complexes, cellular homology
- Euler characteristic, the Lefschetz fixed point theorem
- classification of compact surfaces with and without boundary, orientability

*Algebraic Topology*, covering most of Chapters 0, 1, 2.

## 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