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 | ||
|---|---|---|
| 08/31 | Course Intro
Introduction to the course; What is logic?; statements; disjunction, conjunction, negation; interpretations; truth tables; |
Logical equivalencies; conditional connective; |
| 09/07 | Conditional equivalence contd., biconditional connectives; inverse, converse, contrapositive; "sufficient" and "necessary" conditions; arguments Checking validity of arguments via truth table; rules of inference; proving arguments; |
logic gates; circuits; translating truth tables into statements; translating statements into circuits; |
| 09/14 | building an "addition" circuit; Predicates and domains, | Practice translating English to Predicate Logic; |
| 09/21 | Universal and Existential quantifiers
negating statements, free vs. bound variables; interpretations; rules of inference; empty domains,closure; Why number theory?; basic definitions, |
Introduction to proofs; direct; contrapositive; |
| 09/28 | Midterm Review | Midterm I |
| 10/05 |
contradiction; Equivalence proofs; constructive proofs |
proofs by exhaustion/cases; Universal Generalization proofs Notation for divisibility; Fundamental Theorem of Arithmetic |
| 10/12 | Fall Break (No class) |
Applications of the Fundamental Theorem Modular Congruence, Modular Arithmetic Theorem Floors and Ceilings |
| 10/19 | review of sequences, summations, and products; Introduction to induction; |
induction proofs with congruences; induction proofs with summations |
| 10/26 | Induction with inequalities, Induction with recurrences |
Introduction to strong induction. More examples of strong induction |
| 11/02 | Midterm Review | Midterm II |
| 11/09 | Set Theory definitions (cardinality, subset, 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; Proofs with powersets; Partition of Sets Intro to Combinatorics (Multiplication rule, Permutations) |
Instructor: Mohammad Nayeem Teli (nayeem at cs.umd.edu)
Office: IRB 2224
Office Hours: W 10:00 AM - 11:00 AM
| Name | Email (at umd.edu) | Discussion Lead |
|---|---|---|
| Connie Hong | conniehg | 0101 |
| Despoina Kosmopoulou | despoina | 0102 |
| Wei Liu | wliu283 | 0103 |
| Sijing Yu | sjyu | 0104 |
| Siddhi Patil | scpatil | 0105 |
| Zahra Sodagar | zsodagar | 0106 |
| Monday |
Sijing: 11:00 AM - 3:00 PM, Zahra: 2:00 - 6:00 PM |
| Tuesday |
Siddhi: 9:30 - 11:30 AM |
| Wednesday |
Despoina: 10:30 AM - 12:30 PM, |
| Thursday |
Siddhi: 9:30 - 11:30 AM, Despoina: 3:30 - 5:30 PM |
| Friday |
Connie: 9:00 AM - 1:00 PM, Wei: 1:00 - 5:00 PM |
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.