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 | ||
|---|---|---|
| 08/26 | Course Intro
Introduction to the course; What is logic?; statements; disjunction, conjunction, negation; interpretations; truth tables; logical equivalence |
Logical equivalencies; conditional connective; |
| 09/02 | 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; |
| 09/09 | building an "addition" circuit; Predicates and domains, | Universal and Existential quantifiers negating statements, Practice translating English to Predicate Logic; |
| 09/16 | free vs. bound variables; interpretations; rules of inference; empty domains,closure; Why number theory?; basic definitions, | Introduction to proofs; direct; contrapositive; |
| 09/23 | contrapositive;contradiction; Equivalence proofs | Midterm Review |
| 09/30 | Midterm I | constructive proofs; proofs by exhaustion/cases; |
| 10/07 | Applying Universal Generalization; More proof examples; Notation for divisibility; Fundamental Theorem of Arithmetic , Applications of the Fundamental Theorem | Modular Congruence, Modular Arithmetic Theorem Proof by contradiction; "famous" proofs;
Modular Congruence, Modular Arithmetic Theorem, Quotient-Remainder Theorem, floor and ceiling proofs |
| 10/14 | review of sequences, summations, and products; Introduction to induction; induction proofs with congruences; |
induction proofs with summations Induction with inequalities |
| 10/21 | Induction with recurrences, etc.; Introduction to strong induction. More examples of strong induction |
Set Theory definitions (cardinality, subset, union, intersection, compliment, difference, Venn diagrams, tuples, cartesian product, power set, etc.) |
| 10/28 |
Proving subset relationships; Proving set equality; Properties of sets; |
Midterm II Review |
| 11/04 | Midterm II |
Venn diagrams for finding counterexamples; Proofs with powersets; |
| 11/11 | Partition of Sets Intro to Combinatorics (Multiplication rule, permutations), probability |
r-permutations;Probability Contd. |
| 11/18 | More pratice with counting and probability, multi-sets, probability trees; |
Functions; domain, co-domain, range; injection, surjection, bijection; inverse image, inverse function; Cardinality, countability |
| 11/25 | No class (Online video) | Thanksgiving break |
| 12/02 | Countability contd. Pigeonhole principle |
Generalized pigeon hole principle; binary relations, reflexive, symmetric , transitive |
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 |
|---|---|---|
| Faraz Ghahremani Kooreh | farazgh | 0101 |
| Tianfu Wang | tianfuw | 0102 |
| Shwai He | shwaihe | 0102 |
| Sneha Dharmesh Gathani | sgathani | 0103 |
| Tal Ledeniov | ledeniov | 0103 |
| Roksana Khanom | rkhanom | 0104 |
| Sora Cullen-Baratloo | scullenb | 0105 |
| Parsa Hossein | phoseini | 0105 |
| Shuhao Tan | shuhao | 0106 |
| Zain Ahmed Zarger | zzarger | 0106 |
| Juzheng Zhang | juzheng | 0107 |
| Nitya Raju | nraju | 0108 |
| Monday |
Roksana: 11:00 AM - 1:00 PM Sneha: 11:00 AM- 1:00 PM Zain: 12:00 - 1:00 PM Tal: 2:00 - 4:00 PM Sora: 4:00 - 5:00 PM Tianfu: 4:00 - 5:00 PM |
| Tuesday |
Nitya: 11:00 AM - 1:00 PM Faraz: 11:30 AM - 12:30 PM Sora: 12:30 - 1:30 PM Parsa: 3:30 - 5:30 PM Sora: 4:00 - 5:00 PM |
| Wednesday |
Roksana: 11:00 AM - 1:00 PM Sneha: 11:00 AM- 1:00 PM Zain: 12:00 - 1:00 PM Juzheng: 2:00 - 4:00 PM Sora: 2:00 - 3:00 PM Shuhao: 3:00 - 5:00 PM Tianfu: 4:00 - 5:00 PM |
| Thursday |
Shuhao: 11:00 AM - 1:00 PM Faraz: 11:30 AM - 12:30 PM Parsa: 3:30 - 5:30 PM Juzheng: 2:00 - 4:00 PM |
| Friday |
Faraz: 1:00 - 3:00 PM Nitya: 1:00 - 3:00 PM Tianfu: 2:00 - 4:00 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.