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= CS 303 Discrete Structures = | = CS 303 Discrete Structures = |

## Revision as of 19:49, 17 May 2021

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.

## Contents

# 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

*TODO*

## 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

*TODO*

## Standard resources

CS Programming Assessment Wiki Page

# CS Courses Standard Content Pages

- CS 101 Fundamentals of Computing
- CS 151 Introduction to Computer Science
- CS 170 Web Programming
- CS 201 Computer Science I
- CS 202 Computer Science II
- CS 256 Structured Design
- CS 260 Object Oriented Programming
- CS 303 Discrete Structures
- CS 420 Theory of Computing
- CS 421 Formal Methods
- CS 451 Architecture
- CS452 Software Engineering
- CS 456 Systems Programming
- CS 457 Data Base Processing
- CS 458 Algorithms
- CS 469 Unix/Linux Administration and Networking
- CS 470 Programming Languages
- CS 471 Operating Systems
- CS 473 Networking
- CS 479 Web Programming II
- CS 499 Senior Seminar

# CS 303 Discrete Structures

## Catalog Description

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.

## Prerequisites

- Willingness to work hard.

## Standard Content

### Course Outline

- 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.)
- Basic set theory: sets, intersection, union, complement, Venn diagram, inclusion-exclusion principle (R. Ch. 2)
- 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.)
- Counting: permutations, combinations, binomial theorem, identities (e.g. {Pascal’s identity) pigeonhole principle and applications, double counting (R. Ch. 6)
- Discrete probability: sample space, events experiments, outcomes, distributions, conditional probability, random variables, independence, expectation, linearity of expectation (R. Ch. 7)
- Optional topics: Monty Hall problem, 100 prisoners problem, probabilistic method to prove lower bound on Ramsey numbers
- 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)
- Graph theory: basic graph terminology, undirected graphs, bipartite graphs, degree of a vertex, handshaking theorem, matchings, Hall’s marriage theorem (optional) (R. Ch. 10)

### Learning Outcomes

- Capable of constructing rigorous mathematical proofs using direct proof, proof by contradiction, induction, etc.

### Important Assignments and/or Exam Questions

- What is the decryption function for an aﬃne cipher if the encryption function is c = (15p + 13) mod 26?
- 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?
- 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|.
- What is the probability of these events when we randomly select a permutation of 1,2,3,4?
- 1 precedes 4
- 4 precedes 1
- 4 precedes 1 and 4 precedes 2
- 4 precedes 1, 4 precedes 2, and 4 precedes 3
- 4 precedes 3 and 2 precedes 1.

- 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.)
- Prove by induction that for any positive integer n, the inequality (1 + x)n ≥ 1 + nx holds for all x ∈ R with x > −1.
- 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).