## Courses and Workshops for Bright Kids

We are excited about our reasoning-based mathematics curriculum and our Olympic training workshops. Whether sought for comprehensive education or relied upon for focused study, Olympic preparation or simply enrichment, reasoning-based instruction delivers constructive understanding of mathematics. Our Winter-Spring 2012 offerings are as follows.

**Arithmetic, Algebra and Elements of Analysis:**Mondays and Thursdays 1600-1730 ET, January 9 - March 8, 2012, $459.

*Prior familiarity with algebraic concepts a plus. Material expected to include:*

- Relations and functions, odd, even, 1-1, onto, partial, total, composition, inverse
- Numbers and variables, linear equations, polynomials, exponentials, logarithms
- (Relative) primes, factors, (integer, rational, real and complex) roots
- Key Theorems: Arithmetic, Algebra, Factor, Remainder, Intermediate Value
- Sequences, series, convergence, divergence, limits
- Tangents, areas and volumes, introduction to differentiation and integration

**Counting and Probabilities, Sets and Cardinalities:**Mondays and Thursdays 1600-1730 ET, March 12 - May 3, 2012, $408.

*Mathematical inclination a major plus. Material expected to include:*

- Sets and their operations and measures, membership, union, intersection
- Universal and empty sets, complement, difference, subsets and power sets
- Finite sets and cardinality, counting, permutations, combinations, repetitions
- Probability laws, independent/dependent events, conditional probabilities
- Measures of continuous counting, lengths, areas, volumes, geometric probabilities
- Infinite counting and ℵ
_{0}cardinality - General power set, Cantor's diagonalization, Uncountable sets
- Introduction to probability distributions and densities

**Algebra and Geometry for Younger Bright Kids:**Mondays and Thursdays 1800-1900 ET, January 9 - March 8, 2012, $306.

*Prior familiarity with algebraic concepts a plus. Material expected to include:*

- Natural numbers, addition, number line, lengths and line segments
- Subtraction and integers, directions, multiplication, areas
- Factors, primes, relative primes, factorization
- Lines and angles, forming quadrilaterals, triangles and other figures
- Division and rationals, squares and rectangles
- Using variables, linear equations, tabulation, Cartesian coordinates, graphing and intersects
- Introduction to polynomials, roots and factorization
- Triangles, right triangles, Pythagoras Theorem, irrational numbers
- Circles, π, squaring of the circle

**Elements of Theory of Computation and Complexity and Computer Algorithms:**Tuesdays and Thursdays 1930-2100 ET, January 10 - March 8, 2012, $459.

*Mathematical inclination a plus. Programming experience a plus. Material expected to include:*

- Church's Thesis, Turing-computability, computer languages equivalent to Turing machines
- Limits of computation, the Halting Problem, reductions, Oracles
- Computational complexity and running time of algorithms, NP-completeness, reductions
- Introduction to data structures, scalars, lists, trees
- Common polynomial algorithms: manipulation of data structures, sorting and searching, matrix multiplication

Please review our announcements for more information and contact Dr. Stoyen with any questions or a filled out application form for your bright child.

There are no prerequisites and any mix of courses may be selected. Sessions incorporate instruction, Q&A and discussion, and are live and interactive via WizIQ. Sessions are recorded and available for review or catching up in case of a missed class. Homework emphasizes concept understanding (vs. mere repetition). Fees include instruction, course materials, a performance report and a completion certificate. All sessions are offered subject to sufficient demand. Additional sessions may be scheduled still in the Winter-Spring 2012 and schedules are subject to adjustments and changes.