05/15/19 Today (Wednesday) will be the last day for office hours. Also, the window for regrade requests has passed. Please focus your attention on preparing for the final exam.
Final Exam information:
The final exam is on Saturday 05/18 from 4:00PM to 6:00PM in room SKN 0200. Please arrive at 3:50PM. All students must bring a photo ID to the exam.
04/18/19 Homework #10 has been posted.
04/13/19 Homework #9 has been posted.
04/11/19 Clarification for HW #8: Drawing a Venn Diagram is not a "proof" of any of the claims in the Homework. Also... I showed how you can sometimes use a Venn Diagram to help find a particular counterexample to a false claim, but the Venn diagram itself is not a counterexample.
04/05/19 Homework #8 has been posted.
03/31/19 Homework #7 is due on Friday 4/5. (I accidentally posted the wrong date in one place.)
03/29/19 Homework #7 has been posted.
03/19/19 Homework #6 has been posted.
03/05/19 Homework #5 has been posted.
02/26/19 Homework #4 has been posted.
02/26/19 Regarding HW #3: You do not need to "prove" something like "13 is prime". You can just assert that 13 is prime. However, rather than just asserting something like "72 is composite", I'd like you to write "72 is composite, because 72 = 12 * 6".
02/20/19 Homework #3 has been posted.
02/12/19 Homework #2 has been posted.
02/06/19 On Homework #1, question 7: The expression "t" appears. This is meant to be a variable, not the symbol for "tautology". Sorry for the confusion, it was a bad choice.
02/05/19 The Maryland Center for Women in Computing (MCWIC) will be offering free tutoring for all students in this course. Both 1 on 1 and "guided study sessions" are available. Tutoring will be in room 3136 A.V. Williams starting on February 11th. Guided Study Sessions for this course will be held on Mondays at 3:30PM and Tuesdays at 5:00PM. To sign up for 1 on 1 tutoring go to http://go.umd.edu/TutorRequest
02/04/19 Homework #01 is due at 11:00PM on Wednesday 02/13. (The original homework file did not specify a time.)
02/04/19 Homework #01 has been posted! Click the "Assignments" tab for a link to the assignment.
02/04/19 I have created an experimental (fake) assignment on our course Gradescope account called "Sample Assignment". If you'd like to experiment with the process of submitting an assignment on gradescope, please feel free to submit fake submissions to this assignment. We will ignore them.
02/04/19 You should have received an email inviting you to the course Gradescope account. If you didn't receive this email, send your instructor an email indicating what email address we should use for your account on Gradescope.
01/20/19 This is the class webpage for CMSC250, sections 030X only. Please check here often (at least once a day) for important class announcements.
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.
There is no required textbook for this course and no assignments will refer to a textbook.
For students who like having a textbook as a secondary source of explanations and for practice problems, we recommend "Discrete Mathematics with Applications" by Susanna S. Epp. The book is currently in its 5th edition, but the earlier editions are fine for this course. There are many vendors selling this book online for reasonable prices.
Used books can be very economical, so you might want to find a used copy. You may also find electronic versions of the textbook for less money than a printed copy -- these are fine as well.
Below are links to some of the vendors carrying this book; there are many others, and you may find lower prices from other sources -- shop around. (We are not endorsing any particular sellers.)
There will be numerous homework assignments throughout the semester. The assignments will be distributed, submitted, and graded via GradeScope. Write neatly! If your solutions are not legible you will not receive credit for the assignment. Homework assignments are individual work; you may ask questions of us during office hours but may not work with other students on these assignments. Late homeworks will not be accepted.
Quizzes will not be announced, but you can expect them regularly (nearly every week) during your discussion section.
All students must attend the discussion session for which they are registered; any quiz that is handed in during the wrong section will not be graded.
Final grades will be computed according the following weights.
The following are examples of academic integrity violations that could occur during Computer Science courses:
Use of electronic devices (laptops, tablets, cell phones, etc.) will not be permitted during class, unless the student has an accommodation from the Disability Support Services Unit specifically recommending the use of such a device. Students are expected to take notes during class with pencil and paper.
You are responsible for reading the class announcements that are posted on this webpage. Please check them often (at least once a day). Important information about the course (e.g., deadlines, assignment updates, etc.) will be posted in this section.
The Department of Computer Science takes the student course evaluations very seriously. Evaluations will usually be open during the last few weeks of the course. Students can go to www.courseevalum.umd.edu to complete their evaluations.
Introduction to the course; What is logic?; statements; disjunction, conjunction, negation;
interpretations; truth tables; logical equivalence
Logical equivalencies; conditional and biconditional connectives;
inverse, converse, contrapositive; "sufficient" and "necessary" conditions;
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
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
Introduction to proofs; constructive proofs; proofs by exhaustion/cases; applying Universal
Generalization; styles of proof
More examples; Notation for divisibility; proving implications (directly and
via contrapositive); proving equivalence
Proof by contradiction; "famous" proofs; Fundamental Theorem of Arithmetic
Applications of the Fundamental Theorem, Modular Congruence, Modular Arithmetic Theorem
Quotient-Remainder Theorem, floor and ceiling proofs, review of sequences, summations, and products
Introduction to induction; induction proofs with congruences; induction proofs with summations
Induction with inequalities, recurrences, etc.; Introduction to strong induction.
Lecture 13 Slides
|Spring Break||Spring Break|
More examples of strong induction.
Lecture 14 Slides
Constructive induction and Structural induction; Set Theory definitions (cardinality, subset, union, intersection, compliment, difference, Venn diagrams, tuples, cartesian product
Lecture 15 Slides
Powerset, Proving subset relationships; Proving set equality; Properties of sets; Venn diagrams for
Lecture 16 Slides
Proofs with powersets; partitions; Intro to probability; Multiplication Rule
Lecture 17 Slides
Indpendent events; multiplication rule; probabilities with compliments; addition rule; inclusion/exclusion rule;
decision trees; probability trees
Lecture 18 Slides
Counting techniques: permutations, combinations, tuples, multi-sets, etc.
Lecture 19 Slides
More pratice with counting and probability
Lecture 20 Slides
Functions; domain, co-domain, range; injection, surjection, bijection; inverse image, inverse function;
composition of functions; pigeon hole principle.
Lecture 21 Slides
Relations: binary, ternary, unary, n-ary. Properties of binary relations.
Lecture 22 Slides
Lecture 23 Slides
Using functions to compare cardinalities;
cardinalities of infinite sets; countable vs. uncountable
[There were no slides for this lecture.]
Equivalence relations; partial order relations; total relations and total order relations
Lecture 25 Slides
|Review||[No class this day]|
Office: IRB 2212
Office Hours: Tu/Th 2:10 to 3:10, Fri 11:00-12:00
|Junchi Chu||0301 Discussion Leader||(See table below)|
|Joon Kim||0302 Discussion Leader||(See table below)|
|Deepthi Raghunandan||0303 and 0304 Discussion Leader||(See table below)|
|Roozbeh Bassirian Jahromi||Grader||(See table below)|
|Zhichao Liu||Grader||(See table below)|
|Zehua Zeng||Grader||(See table below)|
|Fei Shan||Grader||(See table below)|
TA office hours will begin on Monday 2/4. 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.
|9:00 - 10:00||Roozbeh|
|10:00 - 11:00||Roozbeh||Fei||Joon||Fei||Roozbeh|
|11:00 - 12:00||Roozbeh||Fei||Joon||Fei|
|12:00 - 1:00||Deepthi||Zehua|
|1:00 - 2:00||Deepthi||Zehua||Zhichao|
|2:00 - 3:00||Zehua||Junchi||Zhichao|
|3:00 - 4:00||Zehua||Junchi||Zhichao|
|4:00 - 5:00||Deepthi||Deepthi||Zhichao|
|Homework #1||Wednesday 02/13||HW 01 Solutions|
|Homework #2||Wednesday 02/20||HW 02 Solutions|
|Homework #3||Wednesday 02/27||HW 03 Solutions|
|Homework #4||Wednesday 03/06||HW 04 Solutions|
|Homework #5||Friday 03/15||HW 05 Solutions|
|Homework #6||Friday 03/29||HW 06 Solutions|
|Homework #7||Friday 04/05||HW 07 Solutions|
|Homework #8||Friday 04/12||HW 08 Solutions|
|Homework #9||Friday 04/19||HW 09 Solutions|
|Homework #10||Friday 04/26||HW 10 Solutions|