## 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.

## Announcements

• Final Exam: Friday, June 10th, 2005, 9-11am in TECH M120. Whole syllabus.

## 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

• Textbooks

Keneth H. Rosen: Discrete Mathematics and Its Applications, Fifth Edition, 2003, McGraw-Hill.

Miguel A. Lerma: Notes on Discrete Mathematics. (See bellow.)

• Problem Sessions

The problem sessions will be held on Tuesdays under the TA's supervision.

• Homework

The homework assignments will be posted on this web page.

• Exams

There will be one one-hour Midterm Exam and one two-hour Final Exam.

• Midterm: Wednesday, May 4rd, 2005, 1:00-1:50pm in TECH M120
• Final: Friday, June 10th, 2005, 9:00-11:00am in TECH M120

No make-up exams will be given. In the event of an extreme and well documented absence (such as hospitalization) the final may be weighted to count for the missing exam. In the case of a missed exam, contact the instructor as soon as possible.

The course will be graded as follows:

• Homework Assignments: 30%
• Midterm: 30%
• Final: 40%

The lowest homework score will be dropped in calculating the homework grade.

If you want to change sections, or add/drop the course, please do so at the CS Department Office.

## 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
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
all