Welcome to CMSC 250. This course covers fundamental mathematical concepts related to computer science, including propositional logic, first-order logic, methods of proof, elementary number theory (including sequences, and induction), set theory with finite and infinite sets, functions, relations, introductory counting and probability theory, and an introduction to graph theory. Emphasis will be on mathematical rigor and the development of sound and elegant formal proofs.
Week Starting | Tuesday | Thursday |
---|---|---|
01/29 | Course Intro
Introduction to the course; What is logic?; statements; disjunction, conjunction, negation; interpretations; truth tables; logical equivalence Introduction Lec01-Examples |
Logical equivalencies; conditional connectives;
"sufficient" and "necessary" conditions;
Lec02 Lec02-Examples |
02/05 |
biconditional connectives;
inverse, converse, contrapositive; arguments
Checking validity of arguments via truth table; rules of inference; proving arguments;
Lec03 Lec03-Examples |
logic gates; circuits; translating truth tables into statements; translating statements into circuits; building an "addition" circuit
Lec04 Lec04-Examples |
02/12 |
Predicates and domains, Universal and Existential quantifiers, negating statements, Practice translating English to Predicate Logic;
Lec05 Lec05-Examples |
truth and falsity of predicates; empty domains, interpretations; translations; negations; rules for negations;
Lec06 Lec06-Examples |
02/19 |
rules of inference; closure; Why number theory?; basic definitions, Introduction to proofs; direct proofs; contrapositive proof;
Lec07 |
contrapositive proof
More examples; proving implications (directly and via contrapositive); proving equivalence
Proof by contradiction;
Lec08 Lec08-Examples |
02/26 | Review
Lec09-Review Lec09-Examples |
Midterm I |
03/05 |
Proofs of Equivalence;
constructive proofs;proofs by exhaustion; Proofs by cases; Constructive proofs of existence;
Lec10 Lec10-Examples |
Proofs by Universal generalization,
divisibility, Fundamental Theorem of Arithmetic,
Applications of the Fundamental Theorem,
Lec11 Lec11-Examples |
03/12 |
Modular Congruence, Modular Arithmetic Theorem,
Quotient-Remainder Theorem, floor and ceiling proofs, Introduction to sequences.
Lec12 Lec12-Examples |
Review of sequences, summations, and products;
Introduction to induction;
Lec13 |
03/19 | Spring Break | |
03/26 |
Induction proofs with congruences; induction proofs with summations
Lec14 Lec14-Examples |
Induction with inequalities, recurrences, etc.; Introduction to strong induction, Examples of strong induction.
Lec15 Lec15-Examples |
04/02 |
More examples of strong induction,
Introduction to Constructive induction
Lec16 Lec16-Examples |
Constructive Induction examples;
Introduction to set theory; definitions (cardinality, subset, etc.)
Lec17 Lec17-Examples |
04/09 |
Review
Lec18-review Lec18-review-Examples |
Midterm II |
04/16 |
Set Definitions Contd. (union, intersection, compliment, difference, Venn diagrams, tuples, cartesian product, power set, etc.)
Proving subset relationships; Proving set equality; Properties of sets; Venn diagrams for finding counterexamples
Lec19 Lec19-Examples |
proofs with rule sheet for set equality; Venn diagrams for counter examples;
Proofs with powersets; partitions; Intro to Combinatorics; Multiplication Rule; permutations
Lec20 Lec20-Examples Lec21 |
04/23 |
r-permutations, combinations, Introduction to discrete probability
Lec22a (P(n,r) and n choose r) Lec22b (discrete probability) |
Joint Probability, Indpendent events; Disjoint events; multiplication rule; probabilities with compliments; addition rule; inclusion/exclusion rule; decision trees;
Lec23 |
04/30 |
multi-sets, probability tree,pigeonhole principle.
Lec24 Lec24-examples pigeonhole principle |
Functions; domain, co-domain, range; injection, surjection, bijection; inverse image, inverse function; composition of functions;
Lec25 Lec25-examples |
05/07 |
Cardinality of infinite sets, countable, uncountable
Lec26 Lec26-examples |
Relations: binary, ternary, unary, n-ary. Properties of binary relations;
Lec27 Lec27-examples |
05/14 | Equivalence relations,partial order relations; total relations and total order relations
Lec28 Lec28-examples |
Instructor: Mohammad Nayeem Teli (nayeem at cs.umd.edu)
Office: 1351 AV Williams
Office Hours: TuTh 1:00 - 2:00 PM
Administrator: Jason Kuo (jkuo147@umd.edu)
Name | Responsibilities | |
---|---|---|
Hamed Kazemi | hamidkazemi22@gmail.com | Grader (0201/0202) |
Seyed Esmaeili | esmaeili@cs.umd.edu | Discussion Lead (0202/0203) |
Dantong Ji | jidantong@gmail.com | Grader (0201/0202) |
Jue Xu | juexu@terpmail.umd.edu | Grader (0201/0202) |
Jason Kuo | jkuo147@umd.edu | Grader (0203) |
Anthony Ostuni | anthonyjostuni@gmail.com | Discussion Lead (0201) |
All TA office hours take place in room 1124 A.V. Williams. Please note that a TA may need to leave 5 minutes before the end of the hour in order to go to his/her class. Please be understanding of their schedules.
Time | MON | TUE | WED | THU | FRI |
---|---|---|---|---|---|
9:00 - 10:00 | |||||
10:00 - 11:00 | Seyed | Dantong | Hamed | ||
11:00 - 12:00 | Seyed | Dantong | |||
12:00 - 1:00 | Hamed | Seyed | Hamed | ||
1:00 - 2:00 | Hamed | Dantong | Seyed | Anthony | |
2:00 - 3:00 | Jue | Dantong | Jue | Anthony | |
3:00 - 4:00 | Jason | ||||
4:00 - 5:00 | Jason | ||||
5:00 - 6:00 |
Homework | Due Date |
---|---|
Homework 1 | 11:59 PM, Tuesday, February 12, 2019 |
Homework 2 | 11:59 PM, Wednesday, February 20, 2019 |
Homework 3 | 11:59 PM, Wednesday, March 13, 2019 |
Homework 4 | 11:59 PM, Thursday, March 28, 2019 |
Homework 5 (pdf,tex) | 11:59 PM, Thursday, April 04, 2019 |
Homework 6 (pdf,tex) | 11:59 PM, Thursday, April 18, 2019 |
Homework 7 (pdf,tex) | 11:59 PM, Thursday, April 25, 2019 |
Homework 8 | 11:59 PM, Thursday, May 2, 2019 |
Homework 9 | 11:59 PM, Thursday, May 9, 2019 |