INTEGRATED ALGEBRA AND GEOMETRY

With Applications to Sports, Arts/Crafts, Genetics, Physics, African Dance, Gardening, Architecture, Interior Design, Business, & Engineering.

Balogun Arinwaka (aka Gary C. Booker), Instructor

Contact Phone: 678-754-0498

Contact email: [email protected]

Please download the following software to be used during this course:

Math Arcade:

http://www.download.com/Math-Arcade/3000-2053_4-10257757.html?tag=lst-0-1

Algebra One on One

http://www.download.com/Algebra-One-on-One/3000-2053_4-2214794.html?tag=lst-0-1

My objectives as an Instructor:

1. To create a nurturing classroom environment where students feel free to engage, knowing they are free to learn from mistakes.

2. To erase Eurocentric bias in the mathematics branch of Algebra that impedes the Process of New Afrikan Youth, which includes (but is not limited to) the omitting of African Geometric concepts from study and the over-credit of discoveries to Europeans.

3. To provide a practical knowledge base on Algebra that can be put to empowering use immediately after taking the course

4. To raise the standard of what is considered, "Algebra II" by including material that should be included in "Algebra II" but isn't taught until most students study precalculus.

Material that will be covered during the course

Module One: Fundamentals:

1. Introduction:

   • What is Algebra?

   • What is Geometry?

   • What is Trigonometry

2. Fundamentals

   • Types of numbers

   • Variables and constants

   • Equations & Functions

   • Rules for solving equations

   • Graphs

   • Monomials

   • Polynomials

3. Addition and Subtraction

   • Properties

   • Polynomial Addition and Subtraction

4. Multiplication and Division

   • Properties

   • Polynomial multiplication and division

   • Factoring Polynomials

   • The Quadratic Formula and the Fundamental Theorem of Algebra

5. Exponents

   • Properties of exponents

   • Exponential equations

6. Radicals

   • Properties of radicals

   • Radical Equations

7. Logarithms

   • Properties of Logarithms

   • Natural Logarithms

   • Logarithmic equations

8. Simplifying expressions and equations

Module Two: Lines & Linear Algebra

9. What is a line?

10. Graphing a line

    • 2D

    • 3D

11. Systems of Linear Equations

12. Parallel, perpendicular lines

    • 2D

    • 3D

13. Vectors

    • 2D

    • 3D

14. Matrices

    • What is a Matrix?

    • Matrix Addition & Subtraction

    • Matrix multiplication

    • Inverse matrices

Module Three: Polygons

15. Triangles & Trigonometry

    • Properties of Triangles

    • Perimeter

    • Area

    • The hypotenuse theorem (c^2 = a^2 + b^2)

    • 30-60-90 Triangles

    • 45-45-90 Triangles

    • The Six Trigonometric Identities

    • The Law of Sines

    • The Law of Cosines

16. Quadrilaterals (Trapezoids, squares, rectangles, rhombi)

    • Properties

    • Perimeter

    • Area

17. Pentagons

    • Properties Perimeter

    • Area

18. Hexagons

    • Properties

    • Perimeter

    • Area

19. Heptagons

    • Properties

    • Perimeter

    • Area

20. Octagons, Nonagons and Decagons

    • Properties of Triangles

    • Perimeter

    • Area

Module Four: Non-linear Functions and their graphs

21. Higher-degree Polynomial Functions

    • Parabolic/Quadratic Equations

    • Cubic Functions

    • Quartic Functions

    • Quintic Functions

22. Exponential Functions

23. Radical Functions

24. Logarithmic Functions

25. Inverse Functions

26. Trigonometric Functions & Trigonometric Identities

Module Five: Circles, Ellipses and Hyperbolas

27. Circles

    • Properties of Circles

    • Circumference of a circle

    • Area of a Circle

    • Chords

    • Secant Lines

    • Tangent Lines

28. Ellipses

    • Properties of Ellipses

    • Circumference of an Ellipse

    • Area of an Ellipse

29. Hyperbolas

30. Polar Coordinates

31. Parametric Equations

Module Six: Three Dimensional Algebra and Geometry

NOTE: Make sure you download graphcalc (http://www.graphcalc.com). You will need it for this module.

1. Planes

2. Sphere

3. Ellipsoid

4. Paraboloid

5. Hyperbolic Paraboloid

6. Elliptic Paraboloid

7. Hyperboloid

8. Cylinder

9. Elliptic Cylinder

10. Parabolic Cylinder

11. Cone

12. Elliptic Cone

13. Triangular Prism

14. Tetrahedron

15. Pyramid

16. Cubes, rectangles and trapezoidal prisms

17. Pentagonal prisms

18. Spherical Coordinates

Module Seven: Complex Variables

32. What are Complex Numbers?

33. Properties of Complex Numbers

    • Addition

    • Subtraction

    • Multiplication

    • Division

34. What are Complex Variables?

35. Properties of Complex Variables

    • Addition

    • Subtraction

    • Multiplication

    • Division

36. Complex Polynomials

Module Eight: Set Algebra & Topology

37. What are sets? What is topology?

38. Venn Diagrams

39. Properties of Sets

40. The Counting Formula

41. The Klein Bottle

42. The Mobius Strip

43. The Cross Cap

44. The Whitney Umbrella

Module Nine: Real Analysis

45. Summation

46. Riemann Sums

47. Permutation

48. The Binomial Theorem

49. Averages

50. Variance and Standard Deviation

51. Series and Sequences

    • Arithmetic Sequence

    • Geometric Sequence

    • Fibronacci Sequence

    • Padovan Sequence

    • Happy Sequence

    • Abundant Number Sequence

    • Logarithmic Spirals

    • Power Series

    • Taylor Series

52. Combinations.

Module Ten: A Survey of Non-Linear Dynamics and Chaos

53. Dynamical Systems

54. The Butterfly Effect

55. Strange Attractors

56. Chaos Fractals

Along with homework assignments, you should expect to do labs. You may do them as I direct, or you may do them to get ahead if you so choose. The labs are your entertaining, hands-on way of learning the concepts you will learn during class.