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Topics in Algebra II

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Section 1:
Recursion, Sequences, and Applications
1. introduction to recursion and sequences
2. arithmetic and geometric sequences
3. loans and investments
4. the compound interest formula
Section 2:
Functions and their Graphs
5. graphs of functions
6. basic models you must know
7. graphical interpretation of sentences like $\,f(x) = 0\,$ and $\,f(x)\gt 0\,$
8. graphical interpretation of sentences like $\,f(x) = g(x)\,$ and $\,f(x) \gt g(x)\,$
9. composition of functions
Section 3:
Probability
10. advanced set concepts
11. basic probability concepts
12. more probability concepts
13. probability tree diagrams
14. choosing things: does order matter?
15. factorial notation
16. combinations and permutations
Section 4:
Statistics
17. summation notation
18. mean, median, and mode
19. measures of spread
Section 5:
Systems of Equations
20. introduction to systems of equations
21. solving systems using substitution
22. solving systems using elimination
23. simple word problems resulting in a system of equations
Section 6:
Matrices
24. introduction to matrices
25. basic arithmetic with matrices
26. multiplying matrices
Section 7:
Graphical Transformations
27. vertical and horizontal translations (moving up, down, left, and right)
28. vertical and horizontal scaling (stretching and shrinking)
29. reflections and the absolute value transformation
30. graphical transformations: all mixed up
Section 8:
Quadratic Functions and More
31. parabolas
32. equations of simple parabolas
33. quadratic functions and the completing the square technique
34. algebraic definition of absolute value
35. the quadratic formula
36. complex numbers
37. arithmetic with complex numbers
38. equations of circles
Section 9:
Exponential and Logarithmic Functions
39. introduction to logarithms
40. properties of logarithms
41. change of base formula for logarithms
42. introduction to logarithmic functions
43. introduction to exponential functions
Section 10:
Polynomials
44. introduction to polynomials