The seminar is a weekly activity designed to bring interesting problems to the student and solve them collaboratively. Additional theory is taught as needed, and efficient problem solving strategies are explored. The seminars are similar to math circles, except for the fact that we are clearly targeting math contests. We coach students not only for the mathematical content but also for tests skills, time management and decision making to help them achieve the best possible score.

We select problems from a variety of sources or of original design. Under the instructor's advice and guidance, students contribute ideas and partial answers. We believe there is great value in the pool of ideas that emerge during each problem solving seminar.

There is no homework associated with this class, as the main value is in working under the supervision of the instructor and in exchanging problem solving ideas within the group.

The problem selection for the seminars range in difficulty from medium to difficult at each grade level. They are quite unlike school textbook material. We recommend that most students register at their current grade level, not higher. New material is provided for these seminars as we keep teaching them, so that students can maintain this activity as a weekly staple throughout the years. Long term participation at the student's current grade level is the best option for steady and continued progress.

The seminars prepare students for a variety of contests over a longer period of times. Students who persevere will typically also excel at school exams. Specifically, the problem solving seminars prepare consistently for the Math Kangaroo and AMC contests. Students who attend the seminars year after year see no difficulty in obtaining good school grades, excellent SAT scores and many achieve outstanding results in competitive math.

The seminars do not have a syllabus, as our instructional design for these seminars is based on developing problem solving skills rather than on topic-by-topic study. A general list of topics that the problems are based on is:

Grades 3-4
Logic Counting Puzzles Simple Cryptarithms Patterns Roman Numerals Operations Properties of Operations Simplifying Arithmetic Operations Symmetry of Figures Properties of Odd and Even Numbers Reasoning Problems Involving Place Value Consecutive Numbers Calendar Military Time Multiples Sum of Digits Timelines Comparisons Backward Solving Spatial Awareness Simple Orthographic Projections Making Solids from Nets Sets Proportional Thinking Paths, Connections Prime Numbers Factoring into Primes Least Common Multiple Greatest Common Divisor Expanded Form of Numbers Simple Distance, Rate, Time
Grades 5-6
Logic Counting Puzzles Cryptarithms Patterns Using Expanded Form Bases of Numeration Comparisons with Integer Exponents Periodic decimals Decimals to fractions Problems with LCM and GCF Order of Operations Integer Division Remainders Divisibility of Numbers Divisibility of Expressions Reducible and Irreducible Fractions Factoring to Simplify Arithmetic Operations Spatial Awareness Percentages Problems with Rates Quantitative Geometry Problems Training Geometric Observation Paths, Connections, Graphs Parity of Integers Perfect Squares and Cubes Pigeonhole Principle Sums of Consecutive Integers Multi-digit Numbers Simple Identities Comparisons and Approximations Invariants
Grades 7-8
Logic Counting Graph Theory Puzzles Cryptarithms Patterns Modular arithmetic Bases of numeration Reducible/irreducible Fractions Repunits Algebraic Identities Perfect Squares and Cubes Percentages Ratios and Proportions Solid Geometry Paths on Solids Special Triangles Diophantine Equations Geometric Loci Spatial awareness Rate, Distance, Time Geometric Proofs Ordering Problems Invariants Prime numbers in Given Conditions Sum of Digits of a Number Arithmetic Sequences Summation Symbol Telescoping Sums AM-GM Inequality Recursive Sequences Discrete Probability Permutations and Combinations