CS40, UCSB, 2014-06/07: "Foundations of Computer Science" (Wim van Dam)

Copyright 2013/2014 Wim van Dam (UCSB) · It is forbidden to copy, distribute, or transit this work, nor is it allowed to alter, transform, or build upon this work. For example, it is not allowed to upload this document to sites such as coursehero.com.

Announcements

  • 2013-12-11: Welcome to the site of CS40, Summer 2014

General Course Information

  • Course No.: CS 40
  • Course Title: Foundations of Computer Science
  • Total Credits: 4

Catalog Description

  • Propositional predicate logic, set theory, functions and relations, counting, mathematical induction and recursion (generating functions).

Prerequisites

  • CS16 with a grade C or better, and MATH4A with a grade C or better.

Course Goals

    • To explain the basic concepts of discrete mathematics as they arise in computer science and, whenever practical, show how they are applied. Learn mathematical induction and proof techniques. Learn mathematical reasoning.

Professor

    • Wim van Dam
    • vandam@cs.____.___
    • Harold Frank Hall, Room 2151

Teaching Assistants

  • tba

Reader

This course has a required reader that will be available at The Alternative.

Typical Weekly Schedule

  • Tuesday, 11:00--12:20, Phelps 2510: class
  • Wednesday, 11:00--12:20, Phelps 2510: class
  • Thursday, 11:00--12:20, Phelps 2510: class
  • Friday, 11:00--12:20, Phelps 2510: discussion

Grading

There will be 4 Homework assignments, 1 Midterm, and 1 Final. See "Course Schedule" below when these are scheduled during the quarter.

All questions of the HW Assignments, Midterm and Final will be graded using the following scale:

  • 6 points: Exemplary; student applies knowledge with virtually no conceptual or procedural errors
  • 4 points: Adequate; student applies knowledge with no significant conceptual errors and only minor procedural errors.
  • 2 point: Minimal; student applies knowledge with occasional conceptual errors and only minor procedural errors.
  • 0 points: Unsatisfactory; student makes significant conceptual and/or procedural errors when applying knowledge.

Your ultimate score for the course is determined as follows.

  • The 4 Homeworks and 1 Midterm all count for an equal amount; the final counts for 2 Homeworks. This means that your total grade will be determined according to: 4 Homeworks + 1 Midterm + 1 Final = 4/7 + 1/7 + 2/7. In other words, each homework and midterm counts for 1/7th, the final counts for 2/7th.
  • However, during the Final you are allowed to decide whether you want to drop your lowest score among your homeworks and midterms and let your final count for 3/7th, in which case the equality becomes: 3 Homeworks + 1 Midterm + 1 Final = 3/7 + 1/7 + 3/7 or 4 Homeworks + 0 Midterm + 1 Final = 4/7 + 0/7 + 3/7.

Means and Standard Deviations of HWs, MT, and F

The scores for the HWs, MT and F will be normalized before being added together. To calculate your 'normalized score', you take your score, subtract the mean, and divide by the standard deviation. The relevant means and standard deviations will be listed here as the quarter progresses.

Midterm

  • Date, time, location: The Midterm will be tba, between 11:00 and 12:20 in Phelps 1401 (i.e. regular class time and location).
  • Topics: tba
  • Allowed: You are allowed to bring with you one page of notes (letter-sized, double sided, readable by human eyes), drinks, non-noisy food, tissues and a watch.
  • Not allowed: You are not allowed to bring with you: the reader, more than one page of notes, electronic devices, et cetera.
  • Importance/What to expect: For your final grade the Midterm 'weighs' the same as a homework assignment (24 points). You can expect 3 or 4 open questions, and somewhere between 3 and 6 True/False questions.

Academic Honesty

The following applies to every course you attend at UC Santa Barbara (from UCSB Campus Regulations, Chapter VII: "Student Conduct and Discipline"):

It is expected that students attending the University of California understand and subscribe to the ideal of academic integrity, and are willing to bear individual responsibility for their work. Any work (written or otherwise) submitted to fulfill an academic requirement must represent a student’s original work. Any act of academic dishonesty, such as cheating or plagiarism, will subject a person to University disciplinary action. Using or attempting to use materials, information, study aids, or commercial “research” services not authorized by the instructor of the course constitutes cheating. Representing the words, ideas, or concepts of another person without appropriate attribution is plagiarism. Whenever another person’s written work is utilized, whether it be a single phrase or longer, quotation marks must be used and sources cited. Paraphrasing another’s work, i.e., borrowing the ideas or concepts and putting them into one’s “own” words, must also be acknowledged. Although a person’s state of mind and intention will be considered in determining the University response to an act of academic dishonesty, this in no way lessens the responsibility of the student.

Specifically for the current CS40 course this means that

  • You are not allowed to copy or transcribe answers to homework assignments from others or other sources.
  • Although you are allowed to discuss homework assignments with others, you should write down your answers independently. You should always be able to argue and explain your answers when asked for clarifications.
  • During the Midterm and Final Examination no electronics are allowed, additional notes are only allowed to the extent described prior to the test.
  • When you will be unable to hand in the homework in time you should report this to WvD as soon as possible, but always before the deadline. No matter the reason, you will always be asked to present documentation.
  • When in doubt, ask.
  • Students violating the rules of Academic Honesty will receive an "F" for the course and will be reported to the Dean of Students Office.

Course Schedule

Week I (06-24/30): Combinatorics

  • Class topics (Tu): Introduction to CS40; Formalities of CS40; sum and product rules [Reader, §1.1, pages 2--4]
  • Class topics (We): permutations [R, §1.2, pp. 5--10]; combinations, binomials [R, §1.3, pp. 13--22]
  • Class topics (Th): combinations with repetitions [R, §1.4, pp. 25--33]; summary of counting techniques [R, §1.6, pp. 40--41]
  • Discussion topics (Fr): HW1 "Combinatorics"

Week II (07-01/07): Propositional Logic

  • Class topics (Tu): connectives, truth tables [R, §2.1, pp. 45--51]
  • Class topics (We+Th): laws of logic, applications of propositional logic [R, §2.2, pp. 53--64]; rules of inference [R, §2.3, pp. 65--82]
  • Discussion: There will be no Discussion on Friday July 4.

Week III (07-08/14): Propositional and First Order Logic

  • Class topics (Tu): logic and complexity theory, quantifiers [R, §2.4, pp. 84--98]
  • Class topics (We): Midterm on Combinatorics and Propositional Logic (all the material of Week I and II)
  • Class topics (Th): proofs [R, §2.5, pp. 101--114]
  • Discussion topics (Fr):

Week IV (07-15/21): Sets

  • Class topics (Tu): sets and subsets [R, §3.1, pp. 121--132]; set operations, laws of set theory [R, §3.2, pp. 134--144]
  • Class topics (We): Venn diagrams [R, §3.3, pp. 146--148]; transformations of sets [R, §5.1, pp. 156--159];
  • Class topics (Th): relations [R, §5.2, pp. 160--162]; functions and infinity [R, §5.3, pp. 163--164]; countable infinity
  • Discussion topics (Fr):

Week V (07-22/28): Sets, Et cetera; Induction

  • Class topics (Tu): infinity [R, §5.3, pp. 163--164]; countable versus uncountable infinity, Cantor's diagonalization argument
  • Class topics (We): mathematical induction [R, §4.1, pp. 180--196]
  • Class topics (Th): strong induction [R, §4.2, pp. 200--207]; recursive definitions, generalized induction [R, §4.3, pp. 210--224]
  • Discussion topics (Fr):

Week VI (07-29/08-03): Extra material; Final

  • Class topics (Tu): graphs [R, §5.4, pp. 165--169], trees [R, §5.5, pp. 170--175]; more on recursive definitions, generalized induction [R, §4.3, pp. 210--224]
  • Class topics (We): "you and your grade", grade estimation; course evaluation; formalities of the Final
  • Final: Thursday, July 31, 11:00--12:20, Phelps 2510
  • Material: Everything covered in class