Office hours: Wed, Fri, 1:00-2:30.
927 Evans Hall
Our class meets in 122 Wheeler, Tuesdays and Thursdays 3:30-5:00. This is the course home page (address www.math.berkeley.edu/~reb/115). The course has control number 55002 and exam group 19.
Prerequisites: 53 and 54. Divisibility, congruences, numerical functions, theory of primes. Topics selected: Diophantine analysis, continued fractions, partitions, quadratic fields, asymptotic distributions, additive problems.
Math 115 will probably cover roughly chapters 1, 2, 3, 4, and 5 of the textbook. (Divisibility, congruences, quadratic reciprocity, number theoretic functions, Diophantine equations.)
Introduction to the theory of numbers, by Niven, Zuckerman, and Montgomery.
Homework will account for about 40% of the grade.
Midterm 1 will account for about 15% of the grade.
Midterm 2 will account for about 15% of the grade.
The final will account for about 30% of the grade.
Almost all the questions in the midterms or finals will be randomly selected questions from the book similar to homework questions, possibly with the constants in the questions changed. So if you understand how to do all the homework questions you will be able to do all the questions on the exams.
There will be no partial credit for incomplete answers of easy problems on the midterms or final exam. Marks for exams or quizzes will only be changed if there is a clear error on the part of the marker, such as adding up marks incorrectly or forgetting to mark a question. Marks for incomplete answers will never be increased, because this is unfair to students who do not ask for their marks to be increased. I will not increase grades just because someone needs a higher grade to graduate or get into some program.
The final homework grade will be computed from the grades for the 10 best homeworks, so it does not matter much if you forget one or two.
You may use a pocket calculator in the exams. You may also bring one (ordinary sized!) sheet of paper with writing on both sides to the exams. Apart from this one sheet, the exams are "closed book".
The first midterm is on Sept 25.
The second midterm is on Oct 30
The final is on Wed Dec 17, 12:30-3:30 in 180 TAN It will be mostly on the material covered after the second midterm, though there will be some problems on earlier material.
Homework is due by the end of the Tuesday lecture 1 week after it is assigned. Late homework will not be accepted. About half the marks for homework will be based on the number of questions that you made a serious attempt on, and about half will be based on more detailed marking of a few questions.
Note that (H) at the end of a problem in the book means that there is a hint at the end of the book.
| Lecture | Date | Reading | Exercises (Due in class the next Tuesday) |
| 01-02 | Aug 26, 28 | 1.1, 1.2 | Section 1.2: 1ab, 2, 3cde, 4ab, 6, 11, 13, 14, 27, 53 |
| 03-04 | Sep 2, 4 | 1.3, 1.4 | Section 1.3: 3, 7, 10, 16, 24, 25, 26. Section 1.4: 1, 2, 3a. |
| 05-06 | Sep 9, 11 | 2.1, 2.2 | Section 2.1: 3, 5, 9, 10, 16, 27, 30, 38 Section 2.2: 5ad, 14 |
| 07-08 | Sep 16, 18 | 2.3, 2.4 | Section 2.3: 2, 10,14, 32, 39, Section 2.4: 3a, 5, 6,13, 14a, |
| 09-10 | Sep 23,25 | Midterm | |
| 11-12 | Sep 30, Oct 2 | 2.5, 2.6, 2.7 | Section 2.6: 1,3,9,10, Section 2.7: 1, 2, 4, 6, 9, 10 |
| 13-14 | Oct 7,9 | 2.8, 2.9 | section 2.8: 1, 4, 8, 23, 34, 35. Section 2.9: 1, 2, 4, 7 |
| 15-16 | Oct 14,16 | 2.10, 2.11 | Section 2.10: 1, 5, 9. Section 2.11: 1,2, 3, 5, 6, 8, 13. |
| 17 -18 | Oct 21,23 | 3.1-3.2 | Section 3.1: 4, 5, 6a, 7abcd, 11, section 3.2: 3, 4, 8, 9, 10 |
| 19 -20 | Oct 28, 30 | Midterm | |
| 21-22 | Nov 4,6 | 3.3, 3.4 | (Due Nov 13) Section 3.3: 1, 2, 5, 7, 14 (hint: use quadratic reciprocity). Section 3.4: 1,2, 4, 7, 8 |
| 23 | Nov 13 | 3.5 | Section 3.4: 9, 10. Section 3.5: 1, 3, 5, 9, 10 |
| 24-25 | Nov 18,20 | 3.6, 3.7 | Section 3.6: 1, 4,8, 11, 12. 3.7: 3, 4, 6(first 4 lines) Due Dec 2. |
| 26 | Nov 25 | ||
| 27-28 | Dec 2,4 | ||
| Dec 17 12:30-3:30 | --- | Final Exam: 180 TAN |