Math 152

• My office phone: 723-4011
• Email: bump@math.stanford.edu
• Office hours: Mon, Tu, Fri 11-12 (subject to change)
• Course assistant: Minyu Peng, with office hours: 8-10 AM Tu-Th.
• Class notes by Lucas Garron
• There will be two in-class midterms, a final exam.
• Midterm Dates: October 13 and November 12.
• Math 152 will use the book of Niven, Zuckerman and Montgomery, The Theory of Numbers (5-th Edition). A high point of the class will be the quadratic reciprocity law of Gauss, which is a truly deep theorem.
• The following sections all contain material that we will cover, though we will not cover everything in all these sections: 1.2, 1.3, 1.4, 2,1-3, 2.7, 2.8, 2.10, 2.11, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 4.2, 4.3
• After finishing Quadratic Reciprocity I expect there will be time left, and there will be time for a further topic, which will be one of the following: Diophantine equations, Algebraic Number Theory or Partitions.
• I will try to make homeworks due Wednesdays, even though it is not a class day.

The second midterm will emphasize results in Chapter 3 through Section 3.6, and will also cover primitive roots (for prime moduli only). The quadratic reciprocity law will be covered, of course. Regarding the material on quadratic forms, I won't ask any questions about the notion of a reduced binary quadratic forms on the midterm. Much of Section 3.6 is technical, and I will cover some of this material a different way from the book. You do not have to study the proofs of Theorems 3.21 and 3.22 in preparing for the midterm.

Homework Assignments and Lecture Notes

• Due Wednesday, September 30, by 5 PM: P.17 # 2,7,10, 11,51 p.29 # 7,9,19.
• Ideals.
• Due Wednesday, September 30, by 5 PM: P.17 # 2,7,10, 11,51 p.29 # 7,9,19.
• Due Wednesday, October 7: P.40 # 1,3, P.56 # 6,16,18,23 P.62 #10,14.
• Due Wednesday, October 14: Page 71, # 9,10,26,27.
• Due Wednesday, October 21: Page 96 # 4,5, P.106, #1,3,4,18,23, P.126 #2.
• Due Wednesday, October 28: Page 33 # 42, Page 135 #4,10,21,23, Page 140 #10,16,22
• Due Wednesday, November 4: Page 136 # 18, Page 147 # 2,4,13,14,20, Page 169 # 8
• conic.pdf. Notes related to the solution to one homework problem of October 28, and to my lecture of October 29.
• sumsofsquares.pdf. Notes for my lecture of November 3.
• moresumsofsquares.pdf. Notes for my lectures of November 5 and 10.
• Due Wednesday, November 11: Page 154 #1; Page 162 #5,9,10

Final Exam

End of Quarter Announcements

Beyond what we have covered for the second midterm, you will be responsible for the following new sections: 4.2 (arithmetic functions), 4.3 (Mobius inversion) and 8.2 (Dirichlet series). To some extent I have already lectured on these topics. I will lecture more on these sections this week, then turn to something interesting during dead week.

I will not assign new homework to be collected and graded. However you will be responsible for the following problems in the sense that I could ask similar questions on the final.

• Page 192 # 6, 9, 16. Page 195 # 6, 8, 16, 18. Page 387 # 1, 7, 9, 18.

The last problem is due to Ramanujan.

Grades

The first two midterms will have letter grades assigned. The final will not. Instead, a course score will be computed using the first two midterms, final and homework.

The course score will be the maximum of two averages, one of which will use the weights Midterm1 25%, Midterm2 25%, Final 40%, HW 10%, and the other will weight the final less heavily.

Then the course score will be curved to a letter grade as consistently as possible with the letter grades announced after the first midterms.

Here is the curve for the first midterm:

Here is the curve for the second midterm: