2010–2011 Topics

Freshmen

  1. NO CALCULATOR. Number Theory and Divisibility: may include patterns (such as trailing zeros), factors, primes, divisibility rules, prime factors of powers, unique factorization, LCM, GCD, and their relationships.
  2. Counting Basics and Simple Probability: Includes tree type problems, combinations, and permutations, with the emphasis on organized thinking, not using formulas.
  3. NO CALCULATOR. Number bases: including conversion and computation in different bases (bases from 2 to 16); finding the base given some information.
  4. Systems of Linear Equations and Inequalities with Applications: Limited to two variables. May include absolute value and should know vocabulary such as consistent, inconsistent, dependent, independent.

Sophomores

  1. NO CALCULATOR. Quadrilaterals: properties, classification, angle measures and sums, area, diagonals, convex and non-convex, cyclic quadrilaterals, Brahmagupta’s formula, etc.
  2. Geometric Probability: emphasis on the concept of geometric probability rather than on difficult geometry problems. Students are not required to have a comprehensive knowledge of geometry.
  3. NO CALCULATOR. Circles: Standard material including arcs, area, angles, power theorems, inscribed and circumscribed polygons, sectors and segments. Does not include trig nor equations of circles.
  4. Geometric Transformations on a Plane: Includes reflections, rotations, translations, dilations, shears, and compositions in two dimensions.

Juniors

  1. NO CALCULATOR. Modular Arithmetic: may include arithmetic operations in different moduli, divisibility, solving simple linear congruences in one or two variables, Fermat’s Little Theorem, Wilson’s Theorem, and Chinese Remainder Theorem.
  2. Probability: the standard treatment of probability. It may include combinations, permutations, mutually exclusive events, dependent and independent events, and conditional probability. It should not include binomial distribution nor expected value.
  3. NO CALCULATOR. Logarithms and Exponents: May include domain and range, graphing, logarithms with positive bases including natural and base ten logs, emphasis on properties, exponential logarithmic growth and decay, and applications. No complex numbers.
  4. Applications of Matrices and Markov Chains: includes solving large systems of equations, using matrix inverses and using transition matrices (aka Markov Chains).

Seniors

  1. NO CALCULATOR. Diophantine Equations: may include linear Diophantine Equations, systems of linear Diophantine Equations, and contextual problems.
  2. Probability: may include combinations, permutations, mutually exclusive events, dependent and independent events, conditional probability, Bayes Theorem, binomial distribution, expected value, and some simple geometric probability.
  3. NO CALCULATOR. Sequences and Series: including, but not restricted to, sequences and series defined by recursion, iteration, or pattern; may include arithmetic, geometric, telescoping, and harmonic sequences and series. No calculus.
  4. Vector Analytic Graphing: includes two dimensional vector applications, two and three dimensional vectors, equations of lines and planes in space, scalar, inner and cross products, perpendicularly and parallels. distance between lines, points and planes. No calculus.

Orals

  1. Polar Coordinates and Equations. Analytic Geometry, by Fuller and Tarwater. (6th-7th ed: Ch. 7; 5th ed: Ch. 6).
  2. Combinatorics. Introduction to Discrete Mathematics, by Roman, Steven. 4.1-4.8, 5.1-5.2.
  3. Topics in Geometry. Geometry Revisited, by Coxeter and Greitzer. 1.1-1.3.
  4. (TBD). , by . .