Welcome!
Here you will see info about what we did in class, upcoming exams, solutions for past exams, etc.,
CHECK AT LEAST ONCE A WEEK!!
COURSE PAGE WITH SYLLABUS, GRADING SCHEME ETC

Started 8/13/2019
UPDATE PAGE FROM FALL 2018 WITH NOTES AND TEST SOLUTIONS
Use this to refer to what we did last time. The order of the material will be different this time.
I may also add a few and modify some things as we go along.

References:
Discrete Mathematics by Johnsonbaugh ; Introduction to Elementary Number Theory by Raji

Please let me know if you have a partner for class project,
and also if you like any of the proofs on the two squares problem (see below).
I will post more sample proofs soon.

Thursday, 10/17/19.
On monday we will do more examples of proof by induction.
Solutions for Quiz 4.

Quiz 4 problems.

Monday, 10/14/2019
QUIZ 4 ON WEDNESDAY, ON INDUCTION AND SEQUENCES.
Please study notes below and try all exercises.

I will be in office tomorrow (Tuesday) from 2 to 4pm.

Updated Notes from today (REFRESH BROWSER) including review of sequences.

Wednesday, 10/9/2019
Please study notes below and try problems mentioned at the end of the slides.
Updated Notes from today (REFRESH BROWSER) on methods of induction.

Monday, 10/7/2019

Please let me know if you have a partner for class project,
and also if you like any of the proofs on the two squares problem (see below).
I will post more sample proofs soon.

Please study notes below and try problems mentioned at the end of the slides.
Notes from today on methods of induction.

Thursday, 10/3/2019
I have not graded all papers yet. As soon as it is done I will post grade sheet on blackboard and midterm grades on bisonweb.
Solutions for Midterm.

Midterm Exam problems.

Monday, 9/30/19
Regarding which numbers are sums of two squares, there is a theorem by Fermat which states the following:
Every prime of the form 4n+1 (such as 5, 17, 29,...) is a sum of two squares and vice versa.
It doesn't say what the two squares are, though.
Now 11 = 4(2)+3 so of the form 4n+3 and NOT 4n+1. So it cannot be the sum of two squares.
Here is the proof.
You can extend this to all numbers by looking at their prime factorization.

MID-TERM EXAM OCTOBER 2. MORE DETAILS SOON.

STUDY CLASS NOTES, QUIZZES AND THE FOLLOWING:
Try the problems first!
If you want, problems only pdf is available here.
Problems 1,2,3,4,7,8,9,10 of Midterm review problems from 2018
Problems 1,4 of Midterm exam 2018

Wednesday, 9/19/19.
Solutions for Quiz 3.

Quiz 3 problems.

Monday, 9/23/2019
QUIZ 3 ON WEDNESDAY.

Please study notes below and try problems mentioned below.
Updated Notes (REFRESH BROWSER) from today on methods of proofs.
Please try problems 2,3,8,9 from Fall 18 test 1 review.
Prove directly that, for integers m,a,b,n,d, if d divides a (d is a factor of a) and d divides b then d divides ma+nb.

Thursday, 9/19/2019
I have updated Notes from yesterday on methods of proofs.

Wednesday, 9/18/2019
Notes from today on methods of proofs.

Monday, 9/16/19.
Wednesday we will look at more methods of proof.
Solutions for Quiz 2.

Quiz 2 problems.

Thursday, 9/12/2019
QUIZ 2 ON MONDAY. READ NOTES AND TRY PROBLEMS AT END. SOLUTIONS TO PRACTICE PROBLEMS BELOW.
SOLUTIONS TO PRACTICE PROBLEMS in Notes .

QUIZ 2 ON MONDAY. READ NOTES AND TRY PROBLEMS AT END.
Wednesday, 9/11/19
Will post problem solutions by friday.

Updated Notes from class today on logical statements INCLUDING PRACTICE PROBLEMS FOR QUIZ.
YOU MAY NEED TO REFRESH YOUR BROWSER.

Monday, 9/9/19
Updated Notes from class today on logical statements.

Wednesday, 9/4/19
Notes from class today on logical statements.

Solutions for Quiz I.

Quiz I problems.

Monday, 8/26/19
QUIZ I ON WEDNESDAY 8/28
If you read and understand these you should be able to do well in quiz.
Updated Notes from class today (including answers for all problems).
The solution for Pythagoras theorem hw problem is in this handout from last year.

NOTE: I will not be on campus after 12pm tomorrow (thu, 8/22) and friday, 8/23.
I will be in office 10 to 11 instead.

Wednesday, 8/21/19
Updated Notes from class today (including stuff from last year on same topic)