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Update page--Discrete Structures-Fall 2025
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
Text: Discrete Mathematics by Richard Johnsonbaugh, 8th edition, Prentice Hall
Syllabus with schedule of classes and exams, grading scheme (SUBJECT TO CHANGE)
Notes and exams from fall 2025.
Started 8-11-2026
TEST DATES:
Midterm 1: Wednesday, September 30
Midterm 2: Wednesday, November 4
FINAL EXAM DEC 4 FRI, 3.30-5.30PM
TEST 1 (MIDTERM 1) on Wednesday, Sep 30.
ALL OF CHAPTERS 1 & 2 (BOTH 7TH & 8TH ED) EXCEPT 2.3 (resolution proofs)
STUDY CLASS NOTES, CLASSWORK NOTES, QUIZ SOLUTIONS, PRACTICE PROBLEMS POSTED HERE EVERYDAY
Please try first MIDTERM I Version 1 PROBLEMS and then
MIDTERM I Version 1 Solutions.
ALSO: FALL 2017 Test I Solutions
Fall 04 Test I (all except 5)
Fall 06 Test I (all except 7)
Also study these class notes (with solutions included).
Friday, 9-25-26
Today we did some problems on proof by strong induction.
Please read these Notes on Egyptian Fractions (Problem 25, in 2.5).
The rest are in these Notes on Strong Induction.
Please study these old notes on proof by induction and try the exercises in it.
Also study these class notes (with solutions included).
Please read sections 4 of chapter 2 of the textbook (see at the top) on methods of proof:
(mostly the ones marked in blue ; the exercises are about proof by induction) :
2.5: 1, 3, 23.
Wednesday, 9-23-26
Today we did a problem on proof by induction and then started talking about strong induction.
Please read Notes on Strong Induction.
Please study these old notes on proof by induction and try the exercises in it.
Also study these class notes (with solutions included).
Please read sections 4 of chapter 2 of the textbook (see at the top) on methods of proof:
(mostly the ones marked in blue ; the exercises are about proof by induction) :
2.4: 1, 4, 7, 13, 16, 18, 19, 22, 26.
Monday, 9-21-26
Please read solutions for quiz. We will start new topic wednesday.
Quiz 4 Problems
Quiz 4 Solutions
Friday, 9-18-26
QUIZ 4 on Monday 9/21. It will cover proof by cases and proof by induction.
Please try problems from 2.2 and 2.4 mentioned this week, below.
Today continued discussing proof by induction.
Please study these old notes on proof by induction and try the exercises in it.
Also study these class notes (with solutions included).
Please read sections 4 of chapter 2 of the textbook (see at the top) on methods of proof:
(mostly the ones marked in blue ; the exercises are about proof by induction) :
2.4: 1, 4, 7, 13, 16.
Wednesday, 9-16-26
QUIZ 4 on Monday 9/21. More details soon.
Today started discussing proof by induction.
Please study these old notes on proof by induction and try the exercises in it.
Also study these class notes (with solutions included).
Please read sections 4 of chapter 2 of the textbook (see at the top) on methods of proof:
(mostly the ones marked in blue ; the exercises are about proof by induction) :
2.4: 1, 4, 7.
Monday, 9-14-26
QUIZ 4 on Monday 9/21. More details soon.
Today we saw some ways to prove mathematical statements using proof by cases.
Please study these old notes on set theory and logic.
Also study these class notes (with solutions included).
Please read sections 2 of chapter 2 of the textbook (see at the top) on methods of proof:
(mostly the ones marked in blue ; the exercises are about proof by cases) :
2.2: 21, 22, 32, 36, 37, 39, 42.
Saturday, 9-12-26
Please read solutions for quiz. We will start new topic friday.
Quiz 3 Problems
Quiz 3 Solutions
Wednesday, 9-9-26
QUIZ 3 on Friday, covering 1.6, 2.1, 2.2
See practice problems below from today and last friday.
Today we saw some ways to prove mathematical statements involving numbers and sets: proof by contrapositive, direct proof.
Please study these old notes on set theory and logic.
Also study these class notes (with solutions included).
Please read sections 1 and 2 of chapter 2 of the textbook (see at the top) on proofs:
(mostly the ones marked in blue ; the exercises are about methods of proof such as direct proof and proof by contrapositive) :
2.1: 7, 10, 14, 16, 21, 24, 33.
2.2: 1, 2, 3, 4, 5, 8, 9.
Friday, 9-4-26
Today we talked about nested quantifiers.
Please study these old notes on set theory and logic.
Also study these class notes (with solutions included).
Please read section 6 of chapter 1 of the textbook (see at the top) on nested quantifiers:
(mostly the ones marked in blue ; the exercises are about nested quantifiers) :
1.6: 39, 40, 41, 42, 43, 48,60, 63.
Thursday, 9-3-26
Please read these notes on quantifiers.
(We did this in class on monday).
Please read solutions for quiz. We will start new topic friday.
Quiz 2 Problems
Quiz 2 Solutions
Monday, 8-31-26
QUIZ 2 on wednesday, 9/2.
Today we saw how to check validity of arguments, and quantifiers.
Please study these old notes on set theory and logic.
Also study these class notes (with solutions included).
Please read section 4 and 5 of chapter 1 of the textbook (see at the top) on arguments and quantifiers:
(mostly the ones marked in blue ; the exercises are about validity of arguments, and quantifiers) :
1.5: 39, 43, 49, 50, 55, 76.
1.4: 15, 18, 30.
Friday, 8-28-26
QUIZ 2 on wednesday, 9/2.
Today we discussed conditional statements, converse, and contrapositive.
Please study these old notes on set theory and logic.
Please read section 3 of chapter 1 of the textbook (see at the top) on basic notions of sets and logical statements do the following exercises:
(mostly the ones marked in blue ; the exercises are about conditional statements) :
1.3: 13, 39, 42, 73, 76.
Wednesday, 8-26-26
Please read solutions for quiz. We will start new topic friday.
Quiz 1 Problems
Quiz 1 Solutions
Monday, 8-24-26
QUIZ 1 on wednesday, 8/26.
Today we discussed DeMorgan's law for sets as well as logic.
We also talked about Venn diagrams, logical statements and did some problems.
Please study these old notes on set theory and logic.
Also read these Worked out examples from fall 25.
Please read section 1 and 2 of chapter 1 of the textbook (see at the top) on basic notions of sets and logical statements do the following exercises:
(mostly the ones marked in blue ; the exercises are about set operations such as union, intersection, etc.,) :
1.1: 1, 4, 7, 10, 13, 16, 17, 23, 35, 47, 61-65, 68, 93.
1.2: 16, 20, 23, 37, 56, 59.
Sunday, 8-23-26
QUIZ 1 on wednesday, 8/26. More details in class.
On friday we discussed briefly about paradoxes, comparing the famous paradoxes of Bertrand Russell and Schrodinger.
We then went over the basics of sets. Please study these old notes on set theory and logic.
Please read section 1 of the textbook (see at the top) on basic notions of sets and do the following exercises:
(mostly the ones marked in blue ; the exercises are about set operations such as union, intersection, etc.,) :
1.1: 1, 4, 7, 10, 13, 16, 17, 23, 35, 47, 61-65, 68, 93.
Wednesday, 8-19-26
Today we discussed a bit more the emerging field of AI generated math.
Following a clip from Tao's talk (see below) we briefly discussed logic, set theory and axioms.
We then talked briefly about paradoxes, starting with the famous paradox of Bertrand Russell.
On friday we will go over the basics of sets. Please study these old notes on set theory and logic.
Saturday, 8-15-26
In our first class we will introduce ourselves, talk about how the course will be structured and provide important information about things you need to pay attention to, throughout the semester.
In remaining time we will discuss the emerging field of AI generated math.
Some questions for you:
What does AI mean?
How does it work?
What are some of the things it can do?
What does it mean for society?
Try to listen to these two talks by Terry Tao, one of the best mathematicians around.
Talk at the International Conference of Mathematicians that just concluded in Philadelphia.
Terry Tao's talk on machine learning and mathematical proofs.
Tuesday, 8-11-2026
Final exam solutions from last fall.
Final exam Version 3 PROBLEMS.
Final exam Version A Solutions.
Final exam Version 3 SOLUTIONS.
Final Exam Version B Solutions.
What we did in first week of fall 2025:
We introduced logic and set theory. We talked about Russell's paradox, how Euclid's parallel lines postulate (that they never intersect)
could not be proved and became an an axiom, and basic set theory.
Notes from class on set theory and logic .
We read section 1 of the textbook on basic notions of sets and did as many exercises as possible.
(Optional) Extra reading related to class:
Here is a How Russell's paradox means there is no set contining all sets
Note on Russell's paradox from 2017.
This note contains its definition, history, and an example using web search principles.
Terry Tao's talk on machine learning and mathematical proofs.
The Dunning-Kruger effect which is about people not knowing what they don't know.