CS 310-0
MATHEMATICAL FOUNDATIONS
OF COMPUTER SCIENCE



Miguel A. Lerma - Spring 2005

Section 20

MWF 1:00 pm - TECH M120

T 1:00 pm - TECH M164


http://www.math.northwestern.edu/~mlerma/courses/cs310-05s/

This is the web page for CS 310, Spring 2005.
Consult it often for announcements, homework assignments and possible changes to the syllabus.


Index


Announcements


Course Description

725-310-0 Mathematical Foundations of Computer Science

Fundamental concepts and tools in discreet mathematics with emphasis on their applications to computer science. Topics include logic and Boolean circuits; sets, functions, relations, databases, and finite automata: deterministic algorithms, randomized algorithms, and analysis techniques based on counting methods and recurrence equations; trees and more general graphs. Prerequisites: 725-110 or 725-111 and 435-214-3. Prerequisite for: 725-322, 725-332, 725-339, 725-343, 725-351.

Learning Goals

At the end of the course, the student should be able to formulate logic expressions for a variety of applications; convert a logic expression into a Boolean circuit, and vice versa; design relational databases; design finite automata to recognize string patterns; apply, adapt, and design elementary deterministic and randomized algorithms to solve computational problems; analyze the running time of non-recursive algorithms with loops by means of counting; analyze the running time of divide-and-conquer recursive algorithms by means of recurrence equations; and use trees and graphs to formulate computational problems.


Teachers

Instructor Teaching Assistant
Name Miguel A. Lerma David Feng
Office Lunt 203 N/A
Phone 1-8020 N/A
E-mail mlerma at math dot northwestern dot edu d-feng@northwestern.edu
Office Hours by appointment
in Lunt 203
TH 12-2pm
in Tech Express
Teaching in TECH M120 TECH M164
Code N.A. TBA


Class Logistics


Lectures and Homework Assignments

Note: I am going to be releasing notes ("Notes on Discrete Mathematics", in PDF format) that you can download by clicking in the links of the "subject" column of the syllabus bellow. The introduction is in here:

Depending on various circumstances, the schedule shown bellow may experiment small modifications.

The "sections" listed on the 4th column are from Rosen's book.

The "Suggested Exercises" column contains some exercises from the book that you may find useful to try. They are not homework nor need to be turned in.

Lect. Date Subject Sections Suggested Exercises Homework
Assignments
Logic, Proofs
1 *Tue 3/29 Propositions 1.1-1.2 1.1: 1,4,7,10,12,21,24,30,32;
1.2: 6,7,9,13-16
2 Wed 3/30 Predicates, Quantifiers 1.3-1.4 1.3: 1-2,5,9,11,12-14,33;
1.4: 1,11,26-28
set 1 - Due Wed 4/6/2005
3 Fri 4/1 Proofs 1.5 1.5: 1,3,5,13-14,21-22,48-52
Sets, Functions, Relations
4 Mon 4/4 Sets 1.6-1.7 1.6: 1-6,13,19,24,27;
1.7: 3-4,14,19,24,33,37-38
Probl. Tue 4/5
5 Wed 4/6 Functions 1.8 1.8: 1-2,4,10-15,19,22-24,31 set 2 - Due Wed 4/13/2005
6 Fri 4/8 Relations 7.1,7.3,7.5-7.6 7,1: 1,34,6-7; 7.3: 1,13-15;
7.5: 1-3,29-30,43;
7.6: 1-5,8-9,16-17,27-29
Algorithms, Integers
7 Mon 4/11 Algorithms, Complexity, Recursiveness 2.1-2.3,3.4-3.5 2.1: 3-4,11-12, 16, 27;
2.2: 1-4,20,21-23;
2.3: 1-2,4,7-8,13-15;
3.4: 1-2,5-8; 3.5: 1-4,16-17
Probl. Tue 4/12
8 Wed 4/13 Division, Euclidean Algorithm 2.4-2.6 2.4: 11-16,28-31;
2.5: 21-24, 2.6: 1-2
set 3 - Due Wed 4/20/2005
9 Fri 4/15 Modular Arithmetic,
The RSA Public-Key Cryptosystem
2.4-2.6 2.4: 25;
2.6: 3-6,11-12,18-19,46-49,59-60
Induction, Recursion
10 Mon 4/18 Sequences, Strings 3.2 3.2: 1-4,9-10,13-18,27-28
Probl. Tue 4/19
11 Wed 4/20 Mathematical Induction 3.3 3.3: 3-4,12-14,18-19,31-32 set 4 - Due Wed 4/27/2005
12 Fri 4/22 Recurrence Relations 6.1-6.2 6.1: 1-4,10-11,42-44;
6.2: 1-4,11-15
Counting
13 Mon 4/25 Combinatorics 4.1,4.3 4.1: 1-6,19-20; 4.3: 1-8,21-24
Probl. Tue 4/26
14 Wed 4/27 More Combinatorics 4.2,4.4-4.5 4.2: 1-4; 4.4: 1-9,33;
4.5: 1-6,14-16,20
(No homework due to the proximity of the Midterm)
Graph Theory
15 Fri 4/29 Graphs 8.1-8.2 8.1: 3-9; 8.2: 1-3,19-23
16 Mon 5/2 Representations of Graphs 8.3 8.3: 1-4,10-12,34-44,61-64
Probl. Tue 5/3
Exam Wed 5/4 MIDTERM EXAM
Answers
up to 5.3
17 Fri 5/6 Paths and Circuits 8.4-8.6 8.4: 1-6,12-13;
8.5: 1-8, 30-43; 8.6: 1-5
set 5 - Due Wed 5/11/2005
18 Mon 5/9 Planar Graphs 8.7-8.8 8.7: 1-9,20-25; 8.8: 1-12
Probl. Tue 5/10
Trees
19 Wed 5/11 Trees 9.1 9.1: 1-2, 11-12 set 6 - Due Wed 5/18/2005
20 Fri 5/13 Binary Trees, Decision Trees 9.2 9.2: 1-6, 23-24, 37
21 Mon 5/16 Tree Transversals 9.3 9.3: 7-19
Probl. Tue 5/17
22 Wed 5/18 Spanning Trees 9.4-9.5 9.4: 2-6, 13-16; 9.5: 1-8 set 7 - Due Wed 5/25/2005
Boolean Algebras
23 Fri 5/20 Boolean Algebras 10.1-10.3 10.1: 1-4,10-11,22-25; 10.2: 1-4; 10.3: 1-6
Automata, Grammars and Languages
24 Mon 5/23 Finite-State Machines 11.2 11.2: 1-4,7-8
Probl. Tue 5/24
25 Wed 5/25 Languages and Grammars 11.1 11.1: 1-8 set 8 - Not Due
26 Fri 5/27 Language Recognition 11.3-11.4 11.3: 10-21; 11.4: 3-4,6-11
Probl. Tue 5/31
27 Wed 6/1 Review for the Final Exam
28 Fri 6/3 Review for the Final Exam
Exam Fri 6/10 FINAL EXAM
Answers
all

(Last Modified: June 10, 2005)

The appendix is here.

The complete set of notes is here. However I do not recommend to download the whole set until the end of the quarter, since I may still make some changes to the notes.


Related links


Last modified: Thu Jul 10, 2008

Email: mlerma at math dot northwestern dot edu

WWW Address: "http://www.math.northwestern.edu/~mlerma/courses/cs310-05s/"

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