Computer Science 243

Discrete mathematics and Functional Programming
Spring 2017
Thomas VanDrunen



Meeting time: MWF 2:15-3:25 pm.
Meeting place: Science 184

Office hours: MTuWF (not Th) 3:30-4:30 pm; Th 9:30-10:30 am and 1:00-3:00 pm.
Contact: 163 Science; 752-5692; Thomas.VanDrunen@wheaton.edu
http://cs.wheaton.edu/~tvandrun/cs243



Syllabus

ML programming guide

Modeling project

Programming assignment turn-in page.



Final exam: Thurs, May 4, 8:00am


Color code:
Green: Background material---read carefully before class. I will not cover this. You are responsible to know it ahead of time.
Magenta: Core material---read before class. I will briefly review and highlight the content, but not lecture on it. Most of our time in class will be spent working on problems from this material.
Cyan: Advanced material---skim before class, read after class. Usually this will be for hard material that I do not expect you to get on a first read. Familiarize yourself with it before class; I will lecture on it
Moon's dayWoden' s dayFrigga's day

Jan 9

Sets. Sets and elements. 1.(1 & 2)
Slides

Review 1.(1-2), read 1.(3-5)
Optional:
Video for course introduction
Video for sections 1.1-3
Video for section 1.4
Video for section 1.5

Jan 11

Set operations; visual verification; intro to ML [time permitting] (3-6)
Slides

Pg 12: 1.3.(11-14, 16)
Pg 16: 1.4.(1-6, 19)
Pg 20: 1.5.(8-11)
Read 1.6-9
Optional:
Video for section 1.6
Video for sections 1.(8 & 9)

Jan 13

Intro to ML; cardinality and Cartesian products. 1.(6-9).
Slides

Pg 26: 1.6.(1-5)
Pg 32: 1.8.(1, 4, 5)
Pg 36: 1.9.(3, 4, 8, 9, 10).
Note that the ML problems should be submitted on paper with the rest of the assignment.
Skim 1.(10&11)
Optional:
Video for sections 1.(10 & 11)
Video for sections 1.(12)

Jan 16

NO CLASS

Jan 18

Making things in ML. 1.(10-13).
Code from class

Pg 36: 1.9.(14 & 16)
Pg 40: 1.10.(1-4)
ML problems should still be submitted on paper
Re-read 1.11 (if necessary), skim 1.(12 & 13).
Read 2.1
Skim 2.2
Optional:
Video for section 2.1
Video for Section 2.2

Jan 20

More about functions in ML. 1.(11-13); List. Introduction to lists. 2.(1 & 2)
Code from class

Pg 48: 1.11.(4, 8, 10)
Pg 50-51: 1.12.(3, 5, 8)
Pg 70: 2.1.(2-4)
Starting with this assignment, submit ML problems electronically
Recommendation: start working on problems from 2.2 assigned next time
Skim 2.3
Read 2.4
Optional:
Video for Section 2.4

Jan 23

More about lists; powersets. 2.(3 & 4)
Code from class

Pg 74: 2.2.(2, 3, 8, 9, 11, 13, 15)
Pg 82: 2.4.(8-12)
Read carefully 2.5
Skim 2.6

Jan 25

A language processor. 2.(5 & 6)
Code from class

Pg 82: 2.4.(14 & 15)
Pg 91: 2.B
Notes on 2.B
Read carefully 3.(1 & 2)
Read 3.(3 & 4)

Jan 27

Proposition. Propositional forms; boolean values; logical equivalence. 3.(1-4)
Slide
Code from class

Pg 102: 3.3.(5 & 6)
Pg 105: 3.4.(2, 4, 8-12)
Read 3.(5-7)

Jan 30

Conditionals. 3.(5-7)
Slides
Code from class

Pg 108: 3.5.(1 & 2)
Pg 114: 3.7.(1, 2, 7, 8, 9, 12, 13)
Read 3.(8 & 9)

Feb 1

Arguments. 3.(8 & 9)
Slides

Pg 119: 3.8.(3 & 5)
Pg 122: 3.9.(3-7)
Read carefully 3.(10 & 11)
Skim 3.(12 & 13)

Feb 3

Predicates; quantification. 3.(10-13)
Code from class

Pg 133: 3.12.(1 & 2)
Pg 135:3.13.(4 & 5)
Read 3.14

Feb 6

Quantification and arguments. 3.14
Slides

Pg 139: 3.14(6-9)

Feb 8

Review

Feb 10

TEST

Feb 13

Proof. Introduction to proofs; subset proofs. 4.(1 & 2)
Slide

Pg 158:4.2.(2-7)
Review 4.(1 & 2)
Read 4.(3 & 4)

Feb 15

Set equality proofs; set emptiness proofs. 4.(3 & 4)

Pg 160: 4.3.(3, 14, 15, 18)
Pg 161: 4.4.(5,6)
Read 4.(5-8)

Feb 17

Conditional proofs. 4.(5-8)

Pg 162: 4.5.(1, 4, 5)
Pg 164: 4.6.(2,5)
Pg 165: 4.7.(1, 6)
Review 2.4, especially Ex 2.4.15
Skim 4.9

Feb 20

NO CLASS

Feb 22

Powersets. 4.9

Pg 174: 4.9.(1, 3, 4, 6)
Skim 4.(10 & 11)

Feb 24

From theorems to algorithms. 4.(10 & 11)

Pg 177: 4.10.(3, 4, 6)
Correction to Ex 4.10.6
Read carefully 5.1
Read 5.(2 & 3)

Feb 27

Relation. Introduction. 5.(1-3)

Practice exercises
Pg 205: 5.3.(8, 10, 12, 13)
Read 5.4
Optional:
Video for section 5.4

Mar 1

Properties of relations. 5.4

Pg 205: 5.3.(5, 6, 11, 14)
Pg 208: 5.4.(3-5, 22, 24, 25, 26)
Pg 212: 5.5.(5, 7, 9, 10)
All above due Mar 13
Read 5.5

Mar 3

Equivalence relations. 5.5

See Mar 1 for assignment
Read 5.(6 & 7)

Mar 6

NO CLASS

Mar 8

NO CLASS

Mar 10

NO CLASS

Mar 13

Transitive closure. 5.(6 & 7)

Pg 217: 5.6.(1&3)
Pg 222: 5.7.(3&5)
Read 5.(8 & 9)

Mar 15

Partial order relations; topological sort. 5.(8 & 9)

Pg 226: 5.8.(1-5)
Pg 231 5.9.(1 & 8)

Mar 17

Review

Mar 20

TEST

Mar 22

Self Reference. Recursive types. 6.(1-3)

Pg 260: 6.2.(6-8, 14-17)
Read 6.4

Mar 24

Structural induction. 6.4

Pg 268: 6.4.(3,4,6,7)
Skim 6.(5 & 6)

Mar 27

Mathematical induction. 6.(5 & 6)

Pg 273: 6.5.(2 & 4)
Pg 278: 6.6.(2 & 3).
Read 6.9 carefully
Skim 6.10

Mar 29

Loop invariants. 6.(9 & 10)

Pg 306: 6.10.(2-5). Due 11/13

Mar 31

More on loop invariants. 6.(10-11)

Read 7 intro and 7.1 carefully
Read 7.2
Skim 7.3
Practice exercises

Apr 3

Function. Introduction. 7.(1-3)

Pg 331: 7.2.(2&3)
Pg 335: 7.3.(3, 4, 8)
Read 7.4
Skim 7.5

Apr 5

Images and inverse images. 7.(4 & 5)

Pg 342: 7.4.(2, 5, 8, 9, 10)
Read 7.(6-8)

Apr 7

Map and filter. Function properties; inverse functions; composition. 7.(6-8)

Pg 346: 7.6.(2, 3, 6)
Pg 351: 7.8.(1, 5, 6)
Programming problems
Skim 7.9

Apr 10

Cardinality. 7.9

Pg 359: 7.9.(1 & 2)

Apr 12

No-credit quiz. Countability. 7.15

Apr 14

NO CLASS

Apr 17

Review

Apr 19

TEST

Apr 21

Map and foldl; modeling functions. 7.(5 & 14)

Programming problems
Read 7.12 carefully
Skim 7.13

Apr 24

Fixed-point iteration. 7.(12 & 13)

Pg 375: 7.13.(1,3)
Skim 6.12
New version of Sec 6.12

Apr 26

Huffman encoding. 6.12

Programming problems

Apr 28

Review