Abstract These are the notes from a freshman mathematics course the authors
team ... Convergence Tests for sequences, series and power series-12?4; 8 ...
FRESH HONORS MATH LECTURE NOTES FROM PRINCETON U., MATH 106 J. GILMAN AND W. P. THURSTON
Abstract These are the notes from a freshman mathematics course the authors team taught in 1990 at Princeton University. It was designed for students who had taken AP calculus but needed a course that gave them more mathematical sophistication along with some calculus review. Many of the topics were non-standard, including iteration, the ”3x+1”-game, cardinal arithmetic, self-similarity and fractals, but it contains as well standard topics such as power series and convergence. These are NOT the same as notes from Geometry and the Imagination that Thurston, Doyle, Conway and Gilman developed around the same time. These notes cover an unusual list of topics at an elementary level and an unusual style. Parts of these notes have been used the Honors Calculus Sequence at Rutgers-Newark. The table of contents lists all twenty-three sections as being on page 3, which is obviously not correct, but has titles, the number of pages, and the chronological order of each section listed. Because these notes contain many typos, they are NOT for general circulation.
Contents 1. Math 106 Notes-9/25; 1 page 2. How to Talk about Functions-9/27 & 9/28; 12 pages + figures 3. Cardinality: Or, What is Infinity? Does it Exist?- 10/2; 2 pages 4. Cardinality: More definitions- 10/4; 3 pages 5. Why does counting work?-10/5; 4 pages 6. Cardinal Arithmetic: Does a + a = 2a?-10/11; 6 pages 7. Sizes-10/12; 2 pages 8. Why counting works: yet another view-10/15; 4 pages 9. What happens when you iterate?-10/18; 8 pages 10. Mid-term Exam-10/25; 4 pages 1
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J. GILMAN AND W. P. THURSTON
11. Sequences and Series: Why does 1.000 = .999?-11/8; 10 pages 12. Math 106 Workshop, by Dror Bar Natan,-11/9; 3 pages 13. Taylor Series-11/15; 8 pages 14. Putting Taylor Series to Use; Part I and Part II-11/27; 5 pages 15. What is e? Does it exist?-11/27 Part II; 12 pages 16. Convergence Tests for sequences, series and power series-12?4; 8 pages 17. Iteration-12/11; 14 pages 18. Self-similarity and fractals-12/6; 5 pages 19. Power series and the radius of convergence-12/6 & 12/11; 12 pages 20. Kneading Theory-12/13; 10 pages 21. A final word on the connection between kneading sequences, iteration and power series-12/18; 3 pages 22. The 3x + 1-game- 12/18; 4 pages 23. Final Exam; 8 pages
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FRESH HONORS MATH
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1. Math 106 Notes-9/25; 1 page 2. How to Talk about Functions-9/27 & 9/28; 12 pages + figures 3. Cardinality: Or, What is Infinity? Does it Exist?10/2; 2 pages 4. Cardinality: More definitions- 10/4; 3 pages 5. Why does counting work?-10/5; 4 pages 6. Cardinal Arithmetic: Does a + a = 2a?-10/11; 6 pages 7. Sizes-10/12; 2 pages 8. Why counting works: yet another view-10/15; 4 pages 9. What happens when you iterate?-10/18; 8 pages 10. Mid-term Exam-10/25; 4 pages 11. Sequences and Series: Why does 1.000 = .999?-11/8; 10 pages 12. Math 106 Workshop, by Dror Bar Natan,-11/9; 3 pages 13. Taylor Series-11/15; 8 pages 14. Putting Taylor Series to Use; Part I and Part II-11/27; 5 pages 15. What is e? Does it exist?-11/27 Part II; 12 pages 16. Convergence Tests for sequences, series and power series-12?4; 8 pages 17. Iteration-12/11; 14 pages 18. Self-similarity and fractals-12/6; 5 pages 19. Power series and the radius of convergence-12/6 & 12/11; 12 pages 20. Kneading Theory-12/13; 10 pages 21. A final word on the connection between kneading sequences, iteration and power series-12/18; 3 pages 22. The 3x + 1-game- 12/18; 4 pages 23. Final Exam; 8 pages
