# 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