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


Friday, 12/13/19.
Grades have been posted on banner. If you have questions please email me. Happy holidays!
Solutions for Final exam.
Final exam problems.


CURRENT GRADES (AS OF 12/2) HAVE BEEN POSTED ON BLACKBOARD.
AFTER GOING TO COURSE PAGE CLICK ON "CONTENT" FOR GRADE SHEET AND ALSO LOOK UNDER "ANNOUNCEMENTS" FOR EXPLANATIONS.

Please complete teacher evaluations. Instructions have been sent.

MY CORRECT EMAIL ADDRESS IS SSITARAMAN@HOWARD.EDU (no bison in it).

FINAL EXAM DEC 6, FRI, 11am to 1pm, usual classroom.
REVIEW THURSDAY 12/5, 2 TO 4 PM IN ROOM 213, ASB-B.
STUDY CLASS NOTES, QUIZZES AND THE FOLLOWING:
Try the problems first!
QUIZ 1 from spring 2019 proofs 2; spring 19 QUIZ I solutions.
Fall 18 Final exam review problems (EXCEPT 5,17,19,20, and 23 to 27) ; Final review problem solutions.
Early Final Exam Fall 2018 (EXCEPT 6,9,10); Early Final solutions.
Final Exam Fall 2018 (EXCEPT 8,9); Final Exam solutions.



Wednesday, 11/6/2019
Updated notes from today (REFRESH BROWSER) on power sums and binomial formula.
Please try the exercises 1 and 2 mentioned in the notes.


Tuesday, 11/5/2019
I have uploaded all the project papers to blackboard.
On course page in blackboard click on "content."
You can read them next week before they are presented.

For now please read your assigned paper and come and meet with me.
If you cannot meet with me by this friday you will lose 30% of grade for the project.
Please don't wait until last minute!
You are also encouraged to read the proof of formula for Pythagorean triplets from last fall.
Use the fall 2018 update page to read it.

Monday, 11/4/2019
On thursday 2 to 4 in my office we will have a problem session on induction.
You can also make up quiz 5 at that time if you wish.

Notes from today on binomial formula.
Please try the problems mentioned in the notes.
Wednesday we will complete the proof of the formula for power sums.

You are also encouraged to read the proof of formula for Pythagorean triplets from last fall.
Use the fall 2018 update page to read it.

Friday, 11/1/19.
On monday we will start discussing binomial formula in preparation to discuss the proof of the sum of k-th powers of 1,2,3,...,n
Article on Proof of formula for power sums by Prof. Pavel Guerzhoy.

Wednesday, 10/30/19.
Solutions for Quiz 5.

Quiz 5 problems.


Monday, 10/28/2019
Quiz 5 on wednesday. Please study notes below.

Project emails will be sent by tonight.

Updated Notes from today (REFRESH BROWSER) including solution for exercises 15 and 16.
Solution for 17 is similar to that of 2; 18 is just a challenge problem.

Wednesday, 10/23/2019
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.

Updated Notes from today (REFRESH BROWSER) including summation of sequences.
Please read sections on summation of arithmetic and geometric sequences, and do exercises 11,15,16,17, and 18.

Monday, 10/21/2019
Updated Notes from today (REFRESH BROWSER) including summation of sequences.
Please read sections on solutions to exercises 6 and 7, summation of natural numbers, and do exercises 13 and 14.

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
GRADE SHEET ON BLACKBOARD

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.
Please read and try all problems in it.

Wednesday, 9/18/2019
Notes from today on methods of proofs.
Please read and try all problems in it.

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.
Please read it and do problem on page 21.

Wednesday, 9/4/19
Notes from class today on logical statements.
Please read it and do problem on page 12.

Thurssday, 8/29/19.
Solutions for Quiz I.

Quiz I problems.


Monday, 8/26/19
QUIZ I ON WEDNESDAY 8/28
Please read notes below including all problems.
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)
Please read and try homework problems.

Tuesday, 8/20/19
I will not be in office today due to some family duties.

Monday, 8/19/19
Notes from class today (including stuff from last year on same topic)
Please read and try problems on last page.