Math 2001 — Spring 2014
Assignments

Last revised: December 10, 2014 at 3:20pm

Warning: This table will change as the semester progresses! Consult the course website for an up-to-date version of this file. If you are viewing this file in a web browser, press reload to make sure you are viewing the most updated version.

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

Read:Scheinerman, §§1–3 (pp. 1–6)

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

HWdue 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

HWdue Mon. Sept. 29:
Assignment 14
Readfor Mon. Sept. 29:
§5 (pp. 15–22)

Week 6

15

September 29

Proofs

HWdue Weds. Oct. 1:
Assignment 15
Readfor Weds. Sept. 29:
§5–§6 (pp. 15–25)

16

October 1

Proofs

HWdue Fri. Oct. 3:
Assignment 16 [ tex ] [ writeLaTeX ]
Readfor Fri. Oct. 3:
§20 (pp. 119–124)

17

October 3

Proof by contradiction

HWdue Mon. Oct. 6:
Assignment 17 [ tex ] [ writeLaTeX ]
Readfor Mon. Oct. 6:
§22 (pp. 135–145)

Week 7

18

October 6

Induction

HWdue Weds. Oct. 8:
Assignment 18 [ tex ] [ writeLaTeX ]
Readfor 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

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

20

October 10

Induction

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

Week 8

21

October 13

Lists and factorial (again)

HWdue Weds. Oct. 15:
Assignment 21 [ tex ] [ writeLaTeX ]

22

October 15

Induction

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

23

October 17

Sets

HWdue Mon. Oct. 20:
Assignment 23 [ tex ] [ writeLaTeX ]
Readfor 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

HWdue Weds. Oct. 22:
Assignment 24 [ tex ] [ writeLaTeX ]
Readfor Weds. Oct. 22:
§14 (pp. 73–76) (again!)

25

October 22

HWdue Fri. Oct. 24:
Assignment 25 [ tex ] [ writeLaTeX ]

26

October 24

HWdue Mon. Oct. 27:
Assignment 26 [ tex ] [ writeLaTeX ]
Readfor 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

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

28

October 29

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

29

October 31

HWdue Mon. Nov. 3:
Assignment 29 [ tex ] [ writeLaTeX ]
Readdue 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

Assignment 32 [ tex ] [ writeLaTeX ]

Week 12

33

November 10

Functions

Assignment 33 [ tex ] [ writeLaTeX ]

34

November 12

Injections, surjections, bijections

Assignment 34 [ tex ] [ writeLaTeX ]

35

November 14

Injections, surjections, bijections

Assignment 35 [ tex ] [ writeLaTeX ]

Week 13

36

November 17

Infinite sets

Assignment 36 [ tex ] [ writeLaTeX ]

37

November 19

Composition and equality of functions

Assignment 37 [ tex ] [ writeLaTeX ]

38

November 21

Cardinality

Assignment 38 [ tex ] [ writeLaTeX ]

Fall break!

Week 14

39

December 1

Counting

Assignment 39 [ tex ] [ writeLaTeX ]

40

December 3

Counting

Assignment 40 [ tex ] [ writeLaTeX ]

41

December 5

Counting

Assignment 41 [ tex ] [ writeLaTeX ]

Week 15

42

December 8

Binomial coefficients

Assignment 42 [ tex ] [ writeLaTeX ]

43

December 10

Binomial coefficients

Assignment 43 [ tex ] [ writeLaTeX ]

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.

5The supplement is hyperlinked. If you cannot access it, download it from the course webpage at http://math.colorado.edu/~jonathan.wise/teaching/math2001-fall-2014

6In each part, you should find a simple formula for the answer that does not use the ∏ symbol. A formula that is more complicated than necessary will not receive full credit.

7On problem 7, just mark the statements true or false. You do not need to write a proof.

8Hint: It may help to look at Exercise 7.16.