## Math 2001 — Spring 2014 Assignments

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All answers must be fully justified in complete sentences, except on problems marked with a dagger (). An expression of the form 3–6 means that the dagger applies to all of problems 3 through 6; something like 7ab means that the dagger applies to parts a and b of problem 7. Solutions to dagger problems should still be justified, but complete sentences are not required and it should be possible to fit the justification in a single line.

Some problems have a footnote with further explanation.

Lecture

Assignment

Week 1

0

 HW: Bring clickers to the first class Read: Syllabus

1

August 25

Syllabus
What is mathematics?
How to read a math text

2

August 27

Mathematical definition

 HW: §3 (p. 6), #1–3, 41, 6, 12, 13a Read: Scheinerman, §4 (pp. 8–13)

3

August 29

Mathematical statements
Propositions, theorems,
and conjectures

 HW: §4 (p. 13), 2adegijk2, 3, 4, 10, 123 Read: Scheinerman, §7 (pp. 25–28)

Week 2

4

September 3

Propositional calculus
Boolean algebra

 HW: §4 (p. 13), #1abcg, 74, supplement 4, #1–2, §7 (p. 28), #1, 4, 7, 10a Read: Scheinerman, §§8 (pp. 33–38)

5

September 5

Lists

 HW: §8 (p. 38), #2, 5, supplement 5,5 #1–2, Read: Scheinerman, §9 (pp. 40–42)

Week 3

6

September 8

Lists

 HW: §8 (p. 38), #9, 16 supplement 6, #1 §9 (p. 42), #1†, 5†, 6, 13 Read: Scheinerman, §10 (pp. 43–50)

7

September 10

Factorials
Sum and product notation

 HW: §9 (p. 42), #8†6, 10, 15abc supplement 7, #1–2

8

September 12

Sets and subsets

 HW: §10 (p. 50), #1abcd,2,3abcdh, 6bd,7d†7 Read: Scheinerman, §11 (pp. 51–54)

Week 4

9

September 15

Sets and subsets

 HW: §10 (p. 50), #1efg,3efg,4,5,6ac, 7abc,14† §11 (p. 54), #1ab†,2ab,6 Read: Scheinerman, §12 (pp. 56–64)

10

September 17

Quantifiers
Operations on sets

 HW: §11 (p. 54), #1ghij†, 2ghij†, 4, 5aeg, 7, 8 supplement 10, #1 Read: §12 (pp. 56–64)

11

September 19

Operations on sets

 HW: §12 (p. 64), #1†, 2, 3, 9, 21†, 258

Week 5

12

September 22

Review

Exam 1

September 23

Midterm exam 1

6–7:15pm (tentative)

All assignments must be typed from now on!

13

September 24

Exam discussion

 HW due Weds., Oct. 1: Write an explanation of why you lost credit for each exam problem on which you did not receive full credit.

14

September 26

LATEX
Meet in DUANG116

 HW due Mon. Sept. 29: Assignment 14 Read for Mon. Sept. 29: §5 (pp. 15–22)

Week 6

15

September 29

Proofs

 HW due Weds. Oct. 1: Assignment 15 Read for Weds. Sept. 29: §5–§6 (pp. 15–25)

16

October 1

Proofs

 HW due Fri. Oct. 3: Assignment 16 [ tex ] [ writeLaTeX ] Read for Fri. Oct. 3: §20 (pp. 119–124)

17

October 3

 HW due Mon. Oct. 6: Assignment 17 [ tex ] [ writeLaTeX ] Read for Mon. Oct. 6: §22 (pp. 135–145)

Week 7

18

October 6

Induction

 HW due Weds. Oct. 8: Assignment 18 [ tex ] [ writeLaTeX ] Read for Weds. Oct. 8: §22 (pp. 135–145) (again!)

 All assignments must submitted via D2L from now on! http://learn.colorado.edu

19

October 8

Induction

 HW due Fri. Oct. 10: Assignment 19 [ tex ] [ writeLaTeX ] Read for Fri. Oct. 10: §20 (pp. 119–124), §22 (pp. 135–145) (again!)

20

October 10

Induction

 HW due Mon. Oct. 13: Assignment 20 [ tex ] [ writeLaTeX ] Read for Mon. Oct. 13: §8 (pp. 33–38), §9 (pp. 40–42) (again!)

Week 8

21

October 13

Lists and factorial (again)

 HW due Weds. Oct. 15: Assignment 21 [ tex ] [ writeLaTeX ]

22

October 15

Induction

 HW due Fri. Oct. 17: Assignment 22 [ tex ] [ writeLaTeX ] Read for Fri. Oct. 17: §10 (pp. 43–51), §12 (pp. 56–64) (again!)

23

October 17

Sets

 HW due Mon. Oct. 20: Assignment 23 [ tex ] [ writeLaTeX ] Read for Mon. Oct. 20: §14 (pp. 73–76)

Week 9

Counting and relations

 Reading: §§14–15 Suggested problems: §14, #1, 4, 6, 12–16, 17 §15, #1, 3, 4, 6–8, 16, 17

24

October 20

 HW due Weds. Oct. 22: Assignment 24 [ tex ] [ writeLaTeX ] Read for Weds. Oct. 22: §14 (pp. 73–76) (again!)

25

October 22

 HW due Fri. Oct. 24: Assignment 25 [ tex ] [ writeLaTeX ]

26

October 24

 HW due Mon. Oct. 27: Assignment 26 [ tex ] [ writeLaTeX ] Read for Mon. Oct. 27: §15 (pp. 78–83)

Week 10

Equivalence relations and functions

 Reading: §§15, 24, 26 Suggested problems: §15, #1, 3, 4, 6–8, 16, 17 §24, #1–4, 8–9, 12, 14–17, 19–24 §26, #1, 6, 8, 11–13

27

October 27

 HW due Weds. Oct. 29: Assignment 27 [ tex ] [ writeLaTeX ] Read for Weds. Oct. 29: §16, up to “Counting Classes/Parts” (pp. 85–86)

28

October 29

 HW due Fri. Oct. 31: Assignment 28 [ tex ] [ writeLaTeX ] Read due Fri. Oct. 31 §15 (pp. 78–83), §16 (pp. 85–88)

29

October 31

 HW due Mon. Nov. 3: Assignment 29 [ tex ] [ writeLaTeX ] Read due Mon. Nov. 3 §20 (pp. 119–124), §22 (pp. 135–145)

Week 11

30

November 3

Review

31

November 5

Exam 2

32

November 7

Bijections

Week 12

33

November 10

Functions

34

November 12

Injections, surjections, bijections

35

November 14

Injections, surjections, bijections

Week 13

36

November 17

Infinite sets

37

November 19

Composition and equality of functions

38

November 21

Cardinality

Fall break!

Week 14

39

December 1

Counting

40

December 3

Counting

41

December 5

Counting

Week 15

42

December 8

Binomial coefficients

43

December 10

Binomial coefficients

44

December 12

Exam 3

TBA

Final exam

1You should write your answer as a mathematical definition. Make sure to emphasize the term being defined with italics or an underline. Your definition may rely on the following concepts, which you do not have to define: natural number, integer, addition, subtraction, multiplication, division, zero, one.

2Be very careful with part (d)!

3Exercise 12b asks you to analyze the sums of consecutive cubes but shows examples of sums of consecutive odd cubes. You should be looking at the numbers 13, 13 + 23, 13 + 23 + 33, 13 + 23 + 33 + 43, etc.

4Also write a precise statement of the Pythagorean theorem.