CSCI 255 Fall 2016
Introduction to Algorithms and Discrete Structures
Archived Class
Charles Cusack
Computer Science
Hope College
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Course Information


Time     9:30-10:50 TR
9:30-10:20 F
Location     VZN 142

Instructor     Chuck Cusack
Email     cusack@hope.edu
Office     VWF 233
Phone     395-7271
Office Hours       MW 9:30-10:30am or by appointment

Textbooks
  • (AIDMA) An Active Introduction to Discrete Mathematics and Algorithms, Version 2.6, Charles Cusack and David Santos, 2015. (PDF)
  • (IDAA) Introduction to the Design and Analysis of Algorithms, 3rd edition, Anany Levitin, Pearson, 2012.

Resources
  • Answers in the back of the book
    AIDMA has solutions to all of the exercises/questions/etc. and you should read them in their entirety as you read the book.
  • Hints in the back of the book
    IDAA has hints to most of the exercises.
  • Me
    See me during office hours, before or after class, or make an appointment at another time.
  • The Computer Science Help Center
    Check the signs in the lab and classroom for hours. The Help Center Assistants should be able to help you with the discrete mathematics topics. Depending on who is there, they may be able to help with some of the algorithms material.

Description An introduction to the design and analysis of algorithms along with some of the discrete mathematical structures that are fundamental to the field of Computer Science. This course builds on the data structures topics from CSCI235 by exploring efficient ways of using them to solve problems. Algorithm analysis topics include best, worst, and average case analysis of iterative and recursive algorithms; asymptotic notation; and solving recurrence relations. Algorithm design techniques include brute force, greedy, divide-and-conquer, transform-and-conquer, dynamic programming, and space/time tradeoff. Discrete structures topics include propositional logic, proof techniques (especially induction), sets, matrices, sequences and summations, and basic combinatorics.

Topics
  1. Foundational Discrete Structures
    1. Propositional Logic, Equivalences, Truth Tables
    2. Sets
    3. Sequences and Summations
    4. Matrices
    5. Basic Counting
    6. Permutations/Combinations
    7. Binomial Coefficients and Identities, including the Binomial Theorem
    8. Pigeonhole Principle
  2. Proof Techniques
    1. Direct, Contraposition, Contradiction
    2. Proof by Induction
  3. Basic Algorithm Analysis
    1. Big-0, Omega, and Theta Notation
    2. Basic Algorithm Analysis (best/average/worst, time/space, wall-clock/CPU/operations)
    3. Complexity Classes
    4. Recursive Definitions/Recurrence Relations
    5. Solving Recurrence Relations
    6. Analyzing Recursive Algorithms/Master Theorem
    7. P/NP/NP-Complete
  4. Algorithm Design Techniques
    1. Brute Force
    2. Greedy
    3. Divide-and-conquer
    4. Decrease-and-Conquer
    5. Transform and Conquer
    6. Dynamic Programming
    7. Space/Time Tradeoff
    8. Backtracking
    9. Branch-and-bound

Expectations
  • You will complete all exercises as you are reading AIDMA.
  • If you don't understand any of the material, including the exercises (even after looking at solutions), you will ask for clarification in class or in my office.
  • You will complete an SRQ for each chapter/section you read from IDAA.
  • You will review all homework assignments after they have been returned so you know how to properly complete all of the problems.

Advice Here are some comments from students who took the course previously.
  • Be prepared to put a lot of work into this class. It definitely is not the easiest class you'll take, but the work is well worth it. You will learn a lot of information in a short amount of time. This is some of the most important stuff you might learn here.
  • Definitely read everything carefully and do the SRQs/exercises. They really help understand the material.
  • Do the readings and all of the assignments. If you stay on top of that stuff, you have the potential to do very well in the course.
  • Make doing the readings and homework your priority over other things, it takes a few rereadings to understand a lot of the material.
  • Make sure you understand all of the homework exercises, especially if you got them wrong the first time around.
  • Be open to meeting with the professor whenever certain material seems confusing.
  • Enjoy it! The course material is challenging and fun!
  • Stay on top of your work - don't fall behind. Read diligently(multiple times).
  • Don't be afraid to ask questions.
  • Be prepared to spend time outside of class thinking about the material even if you are not actually working on something for the class. Regardless of whether or not you personally enjoy the material you need to act like you do outside of class, so that you will think about the material more to understand it better.
  • Do all of the assigned work and go seek out help when you need it.
  • Don't put off the assignments until the night before.
  • Don't try and cram. Give plenty of time for hw because you can get stuck if you don't understand a concept.
  • Be prepared for a lot of work for the first half of the course and make sure to ask questions if you don't understand the material.