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Math 231 FALL 2005, List of lectures
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On this page I will post content of all lectures with reference to the
book. All handouts also will be posted here.
Mon 9/26: How many numbers are between m and n? Section 1.1.
Tue 9/27: How many multiples of k are between m and n? Section 1.1.
Homework!
Wed 9/28: Division and factorization into primes. Section 1.2.
Fri 9/30: Greatest common divisor and least common multiple. Section 1.2.
Mon 10/3: Any common multiple is divisible by the least common multiple.
Notation for sets. Sections 1.2-1.3.
Tue 10/4: Alphabets and languages; set operations. Sections 1.3-1.4.
Wed 10/5: Set operations and their properties. Section 1.4.
New homework!
Fri 10/7: More of set operations. Functions. Sections 1.4-1.5.
Mon, 10/10: Associativity of composition of functions. Sequences.
Sections 1.5-1.6.
We will have QUIZ on Friday, 10/14!!!
Tue, 10/11: Notation for sums, products, unions and intersections.
Section 1.6.
Wed, 10/12: One-to-one correspondences and invertible functions.
Section 1.7. New homework!
Fri, 10/14: One-to-one correspondences coincide with invertible
functions. Section 1.7. We had quiz 1 today.
Here are the solutions.
Mon, 10/17: Inverse images. Introduction to logic.
Sections 1.7, 2.1.
Tue, 10/18: Logic operations and quantifiers. Section 2.1.
Wed, 10/19: Propositional Calculus. Section 2.2.
New homework!
We will have MIDTERM on Monday, 10/24!!!
Fri, 10/21: More of Propositional Calculus. Examples of proofs.
Sections 2.2-2.3.
Mon, 10/24: We had Midterm 1 today.
Here are the solutions.
Tue, 10/25: Relations. Section 3.1.
Wed, 10/26: Digraphs and graphs. Section 3.2.
New homework!
Fri, 10/28: Matrices. Section 3.3.
Mon, 10/31: Matrices and (di)graphs. Equivalence relations.
Sections 3.3-3.4.
We will have QUIZ on Friday, 11/4!!!
Tue, 11/1: Equivalence relations and partitions. Section 3.4.
Wed, 11/2: Equivalence relations and functions. The congruence
modulo p relation. Sections 3.4-3.5. New homework!
Fri, 11/4: More on congruence modulo p. Section 3.5.
We had quiz 2 today.
Here are the solutions.
Mon, 11/7: Loops and Well Ordering Principle. Section 4.1.
Tue, 11/8: Loop invariants. Section 4.1.
Wed 11/9: Mathematical Induction. Section 4.2.
New homework!
Fri 11/11: More of Mathematical Induction. Section 4.2.
We will have MIDTERM next Monday, November 21. There will be no
office hours on Monday, November 21 (due to my leave).
Mon, 11/14: More examples of Mathematical Induction. Section 4.2.
Tue, 11/15: Big Oh Notation. Section 4.3.
Wed, 11/16: Recursive definitions. Section 4.4.
New homework!
There will be NO LECTURE on Tuesday, November 22!
Fri, 11/18: More of Recursive definitions. Section 4.4.
Mon, 11/21: We had Midterm 2 today.
Here are the solutions.
Wed, 11/23: Recurrence sequences. Section 4.5.
New homework!
Mon, 11/28: Second Principle of Mathematical Induction. Section 4.6.
EVALUATIONS on Wednesday, November 30!!!
We will have REVIEW on Wednesday and Friday!
Tue, 11/29: Euclidean algorithm. Section 4.7.
Wed, 11/30: Review, part I. Chapters I-II.
Practice Exam is now available!
The answers are here. ATTENTION: there were
misprints in Problem 3 and in answer to Problem 13!!!