# Math 115 - Introduction to Number Theory

Instructor: Martin Olsson

Lectures: MWF 10-11, Room 71 Evans.

Course Control Number: 54284

Office: 879 Evans

Office Hours: F 11-1.

Required Text: Niven, Zuckerman, and Montgomery, `An introduction to the theory of numbers', Wiley, 5th edition.

The syllabus explaining grading policy and other things is available here.

Problem Set 1, due Wed Sep 8: section 1.2 problems 1ab, 3abc, 4b, 6, 13, 15.

Problem Set 2, due Wed Sep 15: section 1.3, 5, 8, 13, 17, 25; section 1.4: 1, 3. Selected solutions handed out in class, please ask me for a copy if you didn't get one.

Correction to 1.3 problem 17: As was pointed out in class, the problem is incorrect as stated (n=3 gives a counterexample). To correct it, replace `numbers n such that n^2-1 has four positive divisors' with `numbers n>3 such that n^2-1 has four positive divisors'.

Problem Set 3, due Wed Sep 22, section 2.1: 5,6,13,17,23,27,29,43,49.

Problem Set 4, Due Wed Sep 27, section 2.2: 6, 8, 11. Section 2.3: 3, 14, 34, 35. Selected solutions handed out in class, please ask me for a copy if you didn't get one.

Problem Set 5, Due Mon Oct 11, section 2.6: 2, 5, 10.

Problem Set 6, Due Mon Oct 18, section 3.1: 3,4,7,9,11,19.

Some lecture notes on orders of integers Notes.

Here is the proof of the quadratic reciprocity theorem i gave in class QR.pdf.

Problem Set 7, due Mon Oct 25, section 3.2: 2, 7, 10, 17, 20, 22.

Selected solutions from PS 7:Solutions.

Problem Set 8, due Mon Nov 1, section 7.3: 3, 6; section 7.4: 1, 4.

Selected solutions from PS 8:Solutions.

Practice questions with solutions: here.

Problem Set 9, due Mon Nov 15: section 7.7: 1,2, section 7.8 3.

Midterm 2 with solutions Midterm 2.

Problem Set 10, Due Mon Nov 22: section 7.8: 6,7,8,12,13. Solutions.

Problem Set 11, Due Mon Nov 29. Do exercises 1 through 6 from the notes from class: Notes 1 and Notes 2.