ASMS Math Circle

Basic Information:

The ASMS Math Circle meets on Monday and Wednesday evenings from 5:00pm to 6:00 in Mrs. Prokhorova's Room S205.

Calendar:
Syllabus:

I. Graphs.
1. What Is a Graph?
2. The Degree of a Vertex. Isomorphism.
3. Connectivity and Cycles. Trees.
4. Eulerian Graphs.
5. Euler's Theorem.
6. Oriented Graphs.

II.Invariants.
1. Parity.
2. Colorings.
3. Remainders as Invariants.

III. Number Theory.
1. Prime and Composite Numbers.
2. Remainders and Euclid's Algorithm.
3. Decimal Representation and Divisibility Tests.
4. Diophantine Equations.
5. Congruence.
6. Fermat's Little Theorem.
7. Modular Arithmetic.
8. Tricks.

IV. The Pigeonhole Principle.
1. Basic Pigeonhole.
2. Intermediate Pigeonhole.
3. The Pigeonhole Principle in Geometry.
4. The Pigeonhole Principle in Number Theory.

V. Combinatorics.
1. Permutations and Combinations.
2. Pascal's Triangle and Newton's Binomial Theorem.
3. Strategies and Tactics of Counting.
4. Casework.
5. Paths on a Grid.
6. Probability with lengths and areas.
7. Hockey Stick Identity.
8. Binomial Theorem.

VI. Inequalities.
1. Classical Inequalities.
2. The AM-GM Inequality.
3. Cauchy and Chebyshev Inequalities.
4. The Triangle Inequality.
5. Transformations.
6. Induction and Inequalities.

VII. Games.
1. Fundamental Ideas.
2. Symmetry. Winning Positions.
3. A Strategy of Finding Winning Positions.

VIII. Induction.
1. Process and Method of Induction.
2. MMI and Guessing by Analogy.
3. Classical Elementary Problems.

IX. Logical Problems.

X. Constructions and Weightings.

XI. Optimization Problems.
1. The Extreme principle.
2. Semi-invariant.

XII. Geometry Problems.
1.Heron's Formula.
2.Brahmagupta's Formula.
3.Stewart's Theorem.
4.General Polygon Formulas.
5.Cyclic Quadrilaterals.
6.Ptolemy's Theorem.
7.Vectors.

Links:

American Mathematical Competition (AMC)
Alabama Statewide Mathematics Contest
Math League
Mandelbrot Competition

Other Math Circles:

Mobile Math Circle
Harvard Math Circle
San Jose Math Circle
Berkeley Math Circle