Spring 2011: Math 42

I taught this number theory course for non-majors in Spring 2011. I designed and ran the course myself and wrote all problem sets and exams.

Announcements

The semester is over! Thanks for a great class! If you want to pick up your final exam, I'll be in my office 1-3pm on Wednesday, May 18, or you can email me to set up another time.

Class Policies

Here are links to the syllabus, schedule, and suggestions.

Problems of the Day

These problems will be collected daily and drive class discussion. They will be graded purely on whether or not you tried them, but these problems will likely be helpful for the graded problem sets.
Problems due 2/1
Problem due 2/3
Problems due 2/8
Problems due 2/10
Problem due 2/15
Problem due 2/17
Problem due 2/22
Problem due 3/1
Problem due 3/8
Problem due 3/10
Problem due 3/15
Problems due 3/17
Problem due 3/22
Problem due 3/24
Problem due 4/7
Problem due 4/19
Problem due 4/21
Problems due 4/26
Problem due 4/28

Problem Sets

Due 2/8: Problem Set 1 now with Proof solutions
Due 2/15: Problem Set 2 now with Proof solutions
Due 2/24: Problem Set 3 now with Proof solutions
Due 3/10: Problem Set 4 now with Proof solutions
Due 3/17: Problem Set 5 now with Proof Solutions
Due 3/24: Problem Set 6 now with Proof Solutions
Due 4/7: Problem Set 7 now with Proof Solutions
Due 4/19: Problem Set 8 now with Proof Solutions
Due 4/26: Problem Set 9 (which had no proofs, so there are no proof solutions)
Due 5/3: Problem Set 10

Extra Credit

This extra credit problem set is due on May 10.

Exams

Topics for midterm 1 and Solutions
Topics for midterm 2, a Practice Exam with Solutions and Solutions to the Exam
The final exam was on Friday May 13 at 2pm in Wilson 102. Here is a list of topics and a practice exam with solutions. Here are solutions to the exam.

How to Study for the Final

• Come to class May 5 and 10 with questions. These classes will be all review.
• Read over your notes. It may be helpful to recopy statements of theorems we've proved, or even entire proofs.
• Redo problem sets, especially problems you got wrong (and pick up graded assignments on my office door, KH 018, to see what you got wrong!). Do you understand your mistakes now? An especially good problem set to do again is the review pset. Can you do this one without looking at notes?
• Redo the midterms and practice midterms under exam conditions. Do you still remember the "old" stuff?
• When you feel ready, do the practice final under exam conditions. How did it feel? Check your answers.
• Still have questions? Come to office hours, send an email, or look back at your notes.

Resources

• Hendrik Lenstra wrote an interesting article about continued fractions and Pell's equation. He gives details of Archimedes' cattle problem.
• A good reference for continued fractions is chapter 7 in An Introduction to the Theory of Numbers by Niven, Montgomery and Zuckerman. I recommend doing an example while reading the theory--there is quite a lot of notation, so having a concrete example of what's going on may help.
• Keith Conrad has tons of notes on his website. I recommend the notes on Z[i].
• Bruce Ikenaga has number theory notes on his website. I find them wonderfully easy to read, with good examples.
• William Stein generously makes his book freely available online. This book is a little more advanced than our class, but could still be helpful.
• H. Davenport's book, The Higher Arithmetic, is a nice book which I haven't looked at lately. From what I remember, it is a friendly read.
• Joe Silverman's book, A Friendly Introduction to Number Theory, is an extemely gentle book. It has been used for this class in the past.
• The Art of Problem Solving has a wiki aimed mainly at high school students, though it is still highly relevant to our class. (As it is a wiki, beware errors! I have seen egregious errors there in the past.)
• Tom Apostol's book Introduction to Analytic Number Theory, has a nice chapter on generators (he calls them primitive roots), including examples of using logarithms (he calls them indices). In general, this book covers a lot of material that we won't cover, but it's a good book when there's overlap.