CS 310-0
MATHEMATICAL FOUNDATIONS
OF COMPUTER SCIENCE



Miguel A. Lerma - Winter 2004

Section 20

MWF 9:00 am - TECH A110

T 9:00 am - TECH A110


http://www.math.northwestern.edu/~mlerma/courses/cs310-04w/

This is the web page for CS 310, Winter 2004.
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 Pin Ren
Office Lunt 203 Computer Science Dept. Room 230
1890 Maple Ave.
Phone 1-8020 1-3296
E-mail mlerma at math dot northwestern dot edu p-ren@cs.northwestern.edu
Office Hours by appointment
in Lunt 203
TH 1:30-3:30pm
TH 1:30-5:00pm during final week
in CS Dept. Room 230, 1890 Maple Ave.
Teaching in TECH A110 TECH A110
Code N.A. 223


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 introduccion is in here:

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

The "sections" listed on the 4th column are from Johnsonbaugh'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 and Proofs
1 Mon 1/5 Propositions 1.1-1.2 1.1: 20-24, 27-29, 41-46;
1.2: 28-31, 38-39, 43-46
2 Wed 1/7 Quantifiers, Proofs 1.3-1.4 1.3: 17-35; 1.4: 21-25, 32-36
3 Fri 1/9 Mathematical Induction 1.6 1.6: 2-7, 19, 22, 23, 26, 46 set 1 - Due Tue 1/20/2004
The Language of Mathematics
4 Mon 1/12 Sets 2.1 2.1: 1-10, 25-29, 31, 33, 35, 78, 82
Probl. Tue 1/13
5 Wed 1/14 Sequences, Strings 2.2 2.2: 4, 6, 8, 10, 43, 45, 74, 82, 88-92, 96-100
6 Fri 1/16 Relations 2.4-2.6 2.4: 19-24, 29-34; 2.5: 9-14, 30-31; 2.6: 1-6 set 2 - Due Tue 1/27/2004
7 Mon 1/19 Functions 2.8 2.8: 10-15, 19-23, 26-27, 36-37, 56, 78-84
Probl. Tue 1/20
Algorithms
8 Wed 1/21 Algorithms, Recursiveness, Complexity 3.1-3.2,3.4-3.5 3.2: 19-21; 3.4: 8-9, 12-13, 27-28; 3.5: 1-12, 16-25
9 Fri 1/23 The Euclidean Algorithm 3.3 3.3: 1-5, 21-24 set 3 - Due Tue 2/3/2004
10 Mon 1/26 Modular Arithmetic,
The RSA Public-Key Cryptosystem
3.7 3.7: 1-9
Probl. Tue 1/27
Counting
11 Wed 1/28 Combinatorics 4.1-4.2 4.1: 5, 17-20, 28-30, 34-37, 42-46, 60, 62; 4.2: 10-14, 25-29, 31-34, 58-62
12 Fri 1/30 More Combinatorics,
Pigeonhole Principle
4.6-4.8 4.6: 1-3, 7-9, 15-17, 22-24; 4.7: 1, 3-5, 10-11; 4.8: 1-10 set 4 - Due Tue 2/10/2004
13 Mon 2/2 Probability 4.4-4.5 4.4: 11-17, 30-33, 4.5: 1-5, 22-26, 42-45
Probl. Tue 2/3
Recurrence Relations
14 Wed 2/4 Recurrence Relations 5.1-5.2 5.1: 4-8, 37-40, 18-20; 5.2: 14-15, 34-36
Graph Theory
15 Fri 2/6 Graphs 6.1 6.1: 5-10, 17-18, 22, 27-28, 46-48
16 Mon 2/9 Paths and Cycles 6.2-6.3 6.2: 20-21, 28-38, 6.3: 6-15, 25-36
Exam Tue 2/10 MIDTERM EXAM
Answers
up to 5.2
17 Wed 2/11 Representations of Graphs 6.4-6.6 6.4: 1-7; 6.5: 1-3, 7-9, 13-14, 24-25; 6.6: 1-7
18 Fri 2/13 Planar Graphs 6.7 6.7: 6-9, 18-24 set 5 - Due Tue 2/24/2004
Trees
19 Mon 2/16 Trees 7.1-7.2 7.1: 1-4, 24-25,28; 7.2: 22-26
Probl. Tue 2/17
20 Wed 2/18 Spanning Trees 7.3-7.4 7.3: 2,5,7-9; 7.4: 1-5, 21
21 Fri 2/20 Binary Trees 7.5-7.6 7.5: 1,5-8; 7.6: 1-3,6-8,11-15,16-17 set 6 - Due Tue 3/2/2004
22 Mon 2/23 Decision Trees, Tree Isomorphisms 7.7-7.8 7.7: 1-4,9; 7.8: 1-3, 7-12
Probl. Tue 2/24
Boolean Algebras
23 Wed 2/25 Combinatorial Circuits,
Boolean Algebras
9.1-9.3 9.1: 1-3, 22-27, 30-32' 9.2: 1-3, 6-8, 18-19, 21-22; 9.3: 2-5
24 Fri 2/27 Boolean Functions 9.4-9.5 9.4: 1-3, 11-13; 9.5: 1-11 set 7 - Not Due
Automata, Grammars and Languages
25 Mon 3/1 Automata 10.1-10.2 10.1: 1-3, 6-8, 11-13, 21-23; 10.2: 1-6, 13-15, 21-31
Probl. Tue 3/2
26 Wed 3/3 Languages and Grammars 10.3 10.3: 1-3, 7-10, 15-17, 25-27
27 Fri 3/5 Regular Languages 10.4-10.5 10.4: 1-3, 11-13, 21-23; 10.5: 2-4, 7-9
28 Mon 3/8 Review for the Final Exam
29 Wed 3/10 Review for the Final Exam
30 Fri 3/12 Review for the Final Exam
Exam Fri 3/19 FINAL EXAM
Answers
all

(Last Modified: February 10, 2004)

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


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