Scheduled on 2/20 Friday during Recitation hours.
The exam will be based on the materials of Recitations/Quizzes 1--4 that are on Sections 1.1-- 1.3 and half of 1.4 and 2.1-2.2.
Be aware of the Make-up policy in Course Information and Syllabus 230 Sp26. Read through other policies related to the exam as well.
Materials to study
Quizzes, recitations, and my old exams posted below.
If you aim an A, go through lecture notes (posted as files on Class Log) as well.
Review session
The 2/19 Thursday class will be a review session for the exam.
First, we will do Q & A; you bring your own questions and I answer. Next, we can go through my old exams, posted below, quizzes and/or recitation problems
My old exams
Spring 2025 topics were covered in a different order compared to the current semester.
Accordingly, the instructions for some of the questions (and their solutions) are needed to be modified. Be sure to read additional instructions written in purple.
Their solutions will be shared after the review session on 2/19.
Exam 1 Sp25 #1,2,3,5 (Be sure to read additional instructions written in purple) and Exam 1 Sp25 solution the link to the solution, disabled for the moment
Exam 2 Sp25 #1,3 and Exam 2 Sp25 Solution the link to the solution, disabled for the moment
Links to the solutions of my old exams have been posted above, next to each exam.
Scheduled on 4/17 Friday
The exam will be based on the materials corresponding of Recitations/Quizzes 5--10.
Materials to study
Quizzes, recitations, and my old exams posted below.
If you aim an A, go through lecture notes (posted as files on Class Log) as well.
Review session
The 4/16 Thursday class will be a review session for the exam.
First, we will do Q & A; you bring your own questions and I answer. Next, we can go through my old exams posted below, quizzes and/or recitation problems
My old exams
Spring 2025 had three midterms. The specified problems will be relevant to our upcoming midterm 2.
Their solutions will be shared after the review session on 4/16.
Exam 1 Sp25 #4, 5, 6 and Exam 1 Sp25 solution
Exam 2 Sp25 #2, 5a,b and Exam 2 Sp25 Solution
Exam 3 Sp25 #2, 4 (#4 might be challenging. Hint: Every integer is of the form of 3k,3k+1, or 3k+2. Your midterm exam will be easier than this.) and Exam 3 Sp25 Solution
Links to the solutions of my old exams have been posted above, next to each exam.
5/6 Wednesday, 2pm-4pm, RE121 (our usual classroom) IT, 6C7-1
No make-up for the final exam
The final exam will be based on
All the topics on the two midterms; and
Recitations 11-12 and Quizzes 11-12, that is,
5.1 Induction,
4.1 Divisibility (& 4.3 Definition/Notation of a=b (mod m) meaning m | a-b without further details),
9.1 & 9.5 Equivalence Relations and Equivalence Classes
The actual exam questions will be more like 9.5. The materials of 9.1 is important for you to get over the abstraction of the topic "relation" - this could be surprising hard.
Study guide for the Final Exam
For the materials tested on the two midterms:
Midterm 1 and Midterm 2, and my old exams listed above
A question like Midterm 1 #1b(iii) will not be on the final
For the materials NOT tested on the two midterms:
Exam 3 Sp25 and Exam 3 Sp25 Solution
#3, #5(items a--c are about "equivalence relation" and will be on the final as regular problems; item d is about "equivalence classes" and will be on the final as extra credit problem.
Recitation 11 and Quiz 11: All
Recitation 12: All
p1. 4.1 Three relations in modular arithmetic
p4. 9.5 Congruence modulo m is an equivalence relation
p.5. 9.5 Exercises 11 and 13
pp.6--7. Equivalence classes for extra credit problems
Quiz 12: All
See above in pink
For an equivalence relation problem, you will be asked one of two kinds - congruence modulo m (such as Recitation 12, p.4) or 0,1-bit strings (such as Recitation 12, p.5)
The final exam location has changed to IIT Tower, Room 6C7-1.
Special office hours for the final exam week: 5/6 Wed. 12:30-1:30pm at my office RE 105b
Further updates may appear below until the actual exam date.