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| | * [[CS 479 Web Programming II]] | | * [[CS 479 Web Programming II]] |
| | * [[CS 499 Senior Seminar]] | | * [[CS 499 Senior Seminar]] |
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| − | = CS 303 Discrete Structures =
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| − | == Catalog Description ==
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| − | This course is an introduction to discrete mathematics for computer science. The course covers the basic topics from set theory (including functions and relations), logic, number theory, counting, graph theory, and discrete probability. It involves a detailed study of proof techniques. Prerequisite - C or better in CS 201.
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| − |
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| − | == Prerequisites ==
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| − | * Willingness to work hard.
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| − |
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| − | == Standard Content ==
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| − | ===Course Outline ===
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| − | * Logic: proof tables, existential quantification, universal quantification, proposition, propositional function, De Morgan’s law (R. Ch. 1 - “R.” refers to the Rosen book, see below.)
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| − | * Basic set theory: sets, intersection, union, complement, Venn diagram, inclusion-exclusion principle (R. Ch. 2)
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| − | * Proof techniques: direct proof, contrapositive proof, proof by contradiction, weak induction, strong induction (P. Part 2 and R. Ch. 5 - “P.” stands for the “Book of Proof”, see below.)
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| − | * Counting: permutations, combinations, binomial theorem, identities (e.g. {Pascal’s identity) pigeonhole principle and applications, double counting (R. Ch. 6)
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| − | * Discrete probability: sample space, events experiments, outcomes, distributions, conditional probability, random variables, independence, expectation, linearity of expectation (R. Ch. 7)
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| − | * Optional topics: Monty Hall problem, 100 prisoners problem, probabilistic method to prove lower bound on Ramsey numbers
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| − | * Number theory: modular arithmetic division algorithm, modular exponentiation, primes, sieve or Eratosthenes, gcd, lcm, Euclidean algorithm, Bezout’s theorem, inverses, fundamental theorem of arithmetic, solving linear congruences, affine cipher, RSA (R. Ch. 4)
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| − | * Graph theory: basic graph terminology, undirected graphs, bipartite graphs, degree of a vertex, handshaking theorem, matchings, Hall’s marriage theorem (optional) (R. Ch. 10)
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| − |
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| − | ===Learning Outcomes===
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| − | * Capable of constructing rigorous mathematical proofs using direct proof, proof by contradiction, induction, etc.
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| − |
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| − | ===Important Assignments and/or Exam Questions===
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| − | * What is the decryption function for an affine cipher if the encryption function is c = (15p + 13) mod 26?
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| − | * Show that if 7 integers are selected from {1,2,3, ..., 12}, then there must be a pair of these integers with a sum equal to 13. What if only 6 integers are selected rather than 7? Can you still conclude that there must be a pair of these integers with a sum equal to 13?
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| − | * A k-regular graph G is one such that deg(v) = k for all v ∈ G. Prove that if G is a k-regular bipartite graph with k > 0 and the bipartition of G is A and B, then |A| = |B|.
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| − | * What is the probability of these events when we randomly select a permutation of 1,2,3,4?
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| − | ** 1 precedes 4
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| − | ** 4 precedes 1
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| − | ** 4 precedes 1 and 4 precedes 2
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| − | ** 4 precedes 1, 4 precedes 2, and 4 precedes 3
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| − | ** 4 precedes 3 and 2 precedes 1.
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| − | * Let Xn be the random variable that equals the number of tails minus the number of heads when n fair coins are flipped. Compute the expected value of Xn. (Hint: Define a set of a random variables and express Xn in terms of these random variables. Then use linearity of expectation. Explain clearly everything you do.)
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| − | * Prove by induction that for any positive integer n, the inequality (1 + x)n ≥ 1 + nx holds for all x ∈ R with x > −1.
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| − | * Suppose that the domain of the propositional function P(x) consists of the integers −1, 0, and 1. Write out each of these propositions using disjunctions, conjunctions, and negations: (a) ∃xP(x), (b) ∃x¬P(x), (c) ¬∃xP(x), (d) ¬∀xP(x).
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| − |
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| − | === Standard resources ===
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| − | * [https://www.amazon.com/Discrete-Mathematics-Its-Applications-Seventh/dp/0073383090/ref=sr_1_1?dchild=1&keywords=978-0073383095&qid=1621279949&sr=8-1 “Discrete mathematics and its applications”, 7th edition, by Kenneth Rosen. ISBN: 978-0073383095 (R.)]
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| − | * [https://www.people.vcu.edu/~rhammack/BookOfProof/ Book of Proofs (P.)]
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| − | * Experimental resource: [http://www.zybooks.com/ discrete math course of zyBooks]
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Basic Information About CS Courses
Note: as of summer 2018, this document contains information about all courses that are required in the CS or IT majors. Other CS courses are not listed here yet.
Points of Contact
Steve Baker - CS 151, 469, 479
Laci Egri - CS 303, 420
Arash Rafiey - CS 256, 458
Geoff Exoo - CS 456, 471, 473
R.B. Abhyankar - CS 421, 451, 452, 470
Jeff Kinne - CS 170, 202, 260, 499
Rob Sternfeld - CS 101, 201, 457
Prerequisites
CS 151 is prerequisite for - CS 170, 201, 260
CS 170 is prerequisite for - 479
CS 201 is prerequisite for - CS 202, 303, 469, 479
CS 202 is prerequisite for - all 400 level except 469, 479
CS 303 is prerequisite for - CS 420, 421, 457, 458
Math 115 is corequisite for - CS 201
Math 115 is prerequisite for - CS 202, 303
Courses with no prerequisite - CS 151, 256
TODO/Possible New Pages
Items to spin off as standalone videos / tutorials
Editors - vim, emacs, pico, atom. Should be able to edit text files, save changes, make copies.
IDEs - eclipse, MS visual studio. Should be able to create a project, add source files, compile and run, debug.
Debugging - gdb. Should be able to compile with debug information, use gdb to find where seg fault occurs, set breakpoints and look at variable values, step line by line through code.
Unix tools - grep, sed, awk, find, makefiles, unix regular expressions, reading manual and manual organization, pipes, I/O redirection.
Programming Assessment
Catalog Description
Basic C programming and data structures. 5 questions. Must pass with 3 and 2 halves for - passing CS 499 and Cs 685/695/699, getting higher than a C in CS 500, getting a C or higher in CS 202.
Prerequisites
Standard Content
C programming, with one program from five different types:
- Simple program that requires a loop or nested loops.
- Program that scans through text a character at a time to do something.
- Linked list traversal.
- Binary tree traversal.
- Bit operations.
Important Assignments and/or Exam Questions
Standard resources
CS Programming Assessment Wiki Page
CS Courses Standard Content Pages
