COEN 19 / MATH 51 - Fall 2009

Where & When

Class (#51777/#50887) meets in O'Connor 107 from 11:45am to 12:50pm

Syllabus

The course syllabus can be viewed here.

Final Exam

Wed Dec 9 6:30pm–9:30pm (in the usual classroom, O'Connor 107)
(Registrar's schedule)

Goals & Objectives

In this course, students will gain "mathematical maturity" ― in particular the ability to create and comprehend mathematical arguments. We will focus on mathematical arguments in various areas; in each area, students will build up requisite background knowledge (often useful by itself), culminating in the students being able to:

Prove (or disprove) that two propositions are logically equivalent.
Prove that two sets are equal.
Determine if a function is invertible.
Determine the next term in a sequence, total complicated summations, and encrypt and decrypt secret messages.
Count how many passwords are possible given certain constraints, count how many ways one can get particular poker hands, etc.

In addition to learning these various concepts which are useful in their own right, students will achieve our overarching goal: they will be able to read mathematical arguments written by others and they will be able to produce their own proper mathematical arguments ― not only on the primary topics listed above (and others that we will cover in the course), but also on other topics that the students will come upon in the future.

Homework

HW#1 (was due Fri Sep 25)
§1.1: 2,4,6,8,10,18,20,22,28,34

HW#2 (was due Mon Sep 28)
§1.2: 2,10,12,14,16,18,20,31
(solution to §1.2 #12)

HW#3 (was due Wed Sep 30)
§1.3: 2,8,12,20,27

HW#4 (was due Fri Oct 2)
§1.4: 10
§1.5: 3,4,6,8,10

HW#5 (was due Mon Oct 5)
§1.5: 18,20

HW#6 (was due Fri Oct 9)
§1.6: 10,17,18

HW#7 (was due Mon Oct 12)
§2.1: 2,6,12,16,18,22,26,34

HW#8 (was due Wed Oct 14)
§2.2: 4,14,18,20,24,32

HW#9 (was due Wed Oct 21)
§2.3: 4,10,18,28,36,38,40,41

HW#10 (was due Fri Oct 23)
§3.4: 2,6,10,16,18

HW#11 (was due Wed Oct 28)
§3.6: 24,26
Prove the following theorem:
If a,b,c,d, and m are integers with m > 0 and a ≡ b (mod m) and c ≡ d (mod m), then a + c ≡ b + d (mod m) and ac ≡ bd (mod m).

HW#12 (was due Fri Oct 30)
§3.4: 33,34
§3.7: 6,8,10,12,18,19,26

HW#13 (was due Mon Nov 2)
§1.7: 28
§3.4: 32
§3.7: 45,46

HW#14 (was due Wed Nov 4)
§1.7: 22–24,30
§2.4: 4,6,8,10
§3.7: 15,36

HW#15 (was due Wed Nov 11)
§2.4: 14,18,24,34,38,40,42

HW#16 (was due Fri Nov 13)
§4.1: 9,10,18–20,32,48,55
§4.2: 4,10,29

HW#17 (was due Mon Nov 16)
§4.3: 4a,32,34,35

HW#18 (was due Wed Nov 18)
§5.1: 4,6,8,10,12,14,16,20,26,28

HW#19 (was due Fri Nov 20)
§5.2: 4,6,10,12,14,16,18,24,26

HW#20 (due MON NOV 30)
§5.3: 4,6,10,12,16,20,22,26,30,36,40
HW#21 (due WED DEC 2)
§5.4: 4,6,8,12,20,22,33

[ My Home Page | Department of Mathematics and Computer Science | Santa Clara University ]