YEAR 1: Foundations
In this course we study the fundamentals of math: numbers and their operations. Topics include representations of numbers and their building blocks, higher arithmetic, the basics of abstract algebra, geometric concepts and heuristic methods for mental math and estimation.
Course Outline
Part I
1. Positional Based Number Systems
2. The Real Number line
3. Basics of Set theory
4. Counting and Multiplication
5. Division, Euclidean Algorithm
6. Prime Factorization
7. Fractions
8. Decimals
9. Partial Fraction Decomposition
10. Exponentiation and Scientific Notation
11. Powers and Roots
12. Radix fractions
13. Order of Operations
14. Algebraic Expressions and Variables
15. Simplifying Algebraic Expressions
16. Introduction to Functions
17. Sequences and Series
18. Continued Fractions
19. Measurement
20. Ratio and Rate
Part II
1. Polygons
2. The Circle and Radian Measure
3. Pythagorean Theorem
4. Set product, Coordinate plane
5. Euclidean space
6. Distance, Midpoint and Vectors
7. Graph of a Function, Level Sets
8. The Equation of a Line
9. Solving Simple Equations
10. Solving Multi-Step Equations
11. Inequalities and Their Graphs
12. Solving Inequalities
13. Simplifying Complex Expressions
14. Proportions and Percent Equations
15. Probability
16. Data Analysis and Statistics
17. Problem solving techniques.
18. Estimations
19. Mental Math
20. Triangles, Quadrilaterals
Part III
1. 3D Geometry - Shapes
2. 3D Geometry - Measure
3. Special Irrational Numbers
4. Indefinite Continued Fractions
5. Geometric constructions
6. Symmetry and Transformations
7. Permutations
8. Combinatorics
9. Pascals Triangle
10. Modular Arithmetic
11. The Basics of Groups
12. Symmetry Groups
13. Dihedral Groups
14. Groups and the Unit circle
15. The Basics of Rings
16. Euclidean Domains
17. Polynomial Rings
18. The Basics of Fields
19. Finite Fields
20. Applications and Connections of Abstract Algebra