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 |
|---|---|---|
| 08/29 | Course Intro
Introduction to the course; What is logic?; statements; disjunction, conjunction, negation; interpretations; truth tables; logical equivalence |
Logical equivalencies; conditional and biconditional connectives; |
| 09/04 | 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; building an "addition" circuit |
| 09/11 | Predicates and domains, Universal and Existential quantifiers negating statements, empty domains Practice translating English to Predicate Logic; | free vs. bound variables; interpretations; rules of inference; closure; Why number theory?; basic definitions, |
| 09/18 | Introduction to proofs; direct; contrapositive; | contrapositive;contradiction; Equivalence proofs |
| 09/25 | constructive proofs; proofs by exhaustion/cases; proving implications (directly and via contrapositive); proving equivalence | Midterm Review |
| 10/02 | Midterm I | Applying Universal Generalization; More proof examples; Notation for divisibility; Fundamental Theorem of Arithmetic , Applications of the Fundamental Theorem |
| 10/09 | Modular Congruence, Modular Arithmetic Theorem Proof by contradiction; "famous" proofs; Modular Congruence, Modular Arithmetic Theorem | Quotient-Remainder Theorem, floor and ceiling proofs, review of sequences, summations, and products |
| 10/16 | Introduction to induction; induction proofs with congruences; induction proofs with summations | Induction with inequalities, recurrences, etc.; Introduction to strong induction. |
| 10/23 | More examples of strong induction / Constructive Induction | Constructive induction / Set Theory definitions (cardinality, subset, union, intersection, compliment, difference, Venn diagrams, tuples, cartesian product, power set, etc.) |
| 10/30 | Proving subset relationships; Proving set equality; Properties of sets; Venn diagrams for finding counterexamples; Proofs with powersets; Intro to Combinatorics (Multiplication rule, permutations) | Midterm II Review |
| 11/06 | Midterm II | r-permutations; probability |
| 11/13 | Probability Contd. | |
| 11/20 | Thanksgiving break | |
| 04/27 | More pratice with counting and probability, multi-sets, probability trees; |
Functions; domain, co-domain, range; injection, surjection, bijection; inverse image, inverse function; |
| 12/04 | Cardinality, countability Pigeonhole principle |
Pigeonhole principle contd., binary relations, reflexive, symmetric , transitive |
Instructor: Mohammad Nayeem Teli (nayeem at cs.umd.edu)
Office: IRB 2224
Office Hours:
| Name | Discussion Lead | |
|---|---|---|
| Dhruva Sahrawat | dhruva7 at umd.edu | 0201 |
| Roksana Khanom | rkhanom at umd.edu | 0202 |
| Sean Michael McLeish | smcleish at umd.edu | 0203 |
| Elias Prieto | eprieto at umd.edu | 0204 |
| Nengneng Yu | ynn1999 at umd.edu | 0205 |
| Jacob Langille | jlangill at umd.edu | 0206 |
| Zain Ahmed Zarger | zzarger at umd.edu | 0206 |
| Siyuan Peng | peng2000 at umd.edu | 0207 |
| Zora Che | zche at umd.edu | 0208 |
| Geonsun Lee | gsunlee at umd.edu |
| Monday |
Dhruva: 9:00 - 11:00 AM Roksana: 11:00 AM - 12:00 PM Yu: 12:00 - 1:00 PM Roksana / Jacob: 1:00 - 2:00 PM Yu: 4:00 - 5:00 PM |
| Tuesday | Zora: 9:20 AM - 1:20 PM, Elias: 1:30 - 2:30 PM Siyuan: 2:00 - 3:00 PM, |
| Wednesday |
Dhruva: 9:00 - 11:00 AM, Yu / Siyuan: 12:00 - 1:00 PM Jacob: 1:00 - 2:00 PM Geonsun: 1:00 - 2:00 PM Zain: 2:00 - 4:00 PM Yu: 4:00 - 5:00 PM |
| Thursday |
Geonsun: 11:00 AM - 12:00 PM Elias: 12:30 - 1:30 PM Sean: 1:00 - 2:00 PM Sean / Siyuan: 2:00 - 3:00 PM |
| Friday | Sean: 9:00 - 11:00 AM Roksana: 12:00 - 2:00 PM Siyuan: 1:00 - 2:00 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.
| Homework | Due Date* |
|---|---|
| Homework 1 | Thursday Sep. 14, 2023 |
| Homework 2 | Monday Sep. 25, 2023 |
| Homework 3 | Friday Oct. 13, 2023 |