Current Office Hours:

Assignment: Read ADS Chapter 1.1,1.2 for Wednesday

Lecture notes/slides on sets.

Assignment: Read ADS Chapter 1.3 for Friday

I've put up one WebWork "assignment," for learning the WebWork system. This "Orientation" assignment will not count for your grade, and will stay open for at least a week after the semester actually begins.

This is a FREE FOR YOU online homework system. I will be giving some assignments using it over the semester. It isn't hard to use, and will even let you check correctness of your answers before submitting them.

To log in to WebWork, go to:

https://webwork.oer.hawaii.edu/webwork2/Math_301_Fall_2025_Ross/

Your login should be either your UH email address, or the part of that address before the @ sign. For example, if your UH email is myname@hawaii.edu, your login should be myname

Your initial password is your 8 digit UH ID number.

I've created a brief video tutorial for using WebWork on our system. You might find it useful, just note it is for Math301 from an earlier semester.

VIDEO TUTORIAL (controls to control speed)

(Note: no sound in the video.)

Assignment: Read ADS Chapter 4.1, 4.2 for Wednesday

Assignment: Read ADS Chapter 6.1, 7.1 for Friday

Problems from ADS text:

1.1.3/4, 5, 6, 7
1.2.4/5,6 ,8
1.3.4/1deh,4, 5, 9
4.1.5/1d, 1e, 2, 3ab,6
4.2/4a, 4b

Only turn in the underlined problems on Wednesday, September 10

Lecture notes/slides on functions and cardinality

Assignment: Read ADS 7.2-4

PROBLEMS ON CARDINALITY

(due Monday, Sep 22.  Discuss Friday, Sep 19)

Because basic functions, function composition, and so on should be review for you, I will not be asking you to hand in any HW on the basic material (but I will probably give you some webwork on it). However, I will give you some HW on the "countability" material

Assignment:

ADS text 6.1.4/5; 6.3.4/2, 3, 4, 8( (just turn in #8 frmn this group)

Problem: Show that the relation R consisting of all pairs (x,y) such that x and y are bit strings that agree in their first and third bits is an equivalence relation on the set of all bit strings of length three or more. Describe the equivalence classes for this equivalence relation. (Turn this one in!)

(Due Monday, Sep 22.  Discuss Friday, Sep 19)

Lecture notes/slides on relations

(No slides for lectures on induction, but there is a section in the text, 3.7, unfortunately it uses examples from symbolic logic [we haven't done that yet!] and from combinatorics.)

Assignment: Read 3.7 in the ADS text. Skip Examples 3.7.4 and 3.7.8 as we haven't covered that yet.

Problems: ADS text 3.7.4/2, 4, 5, 8, 10 (a great problem!), look at 13. Hand in only #8.

Three additional induction problems (hand in only the third one).

Discuss these September 22 (Monday)

Due (hand in) the two problems I'm collecting on Wednesday, September 24

(Here is the hardcopy produced in that video.)

Reminder: there is a WW assignment due tonight!

HW due today (problems on cardinality, problems from ADS text Ch.6, and the problem on relations above)

HW due today (two problems on induction)

Here are some practice exam questions.

• Watch the videos (by Wednesday, but try to get the first one watched by Monday if you can) =======>

• Start reading the text. We've already done pretty much all of 2.1!

Videos on counting formulas (combinatorics):

• Video 1
  
• Video 1, but faster (recommended!)
• Video 2
  

Slides for these videos

(You might want to downoad these slides and take notes on them as you watch the videos)

Problems:

From ADS text:
2.1.3/8, 9, 12
(discuss Friday, October 3)

2.1.3/ 18, 19
2.2.2/6, 9, 11
2.3.3/6,8,9
2.4.4/1,2,4,6 (we're doing 5 in class),7,11,12,17

Discuss the ones from this group Monday, October 6

Turn in the underlined problems on Wednesday, October 8

Here is the slide of examples that I had up on the screen today (and will use Friday as well)

Class: Continue combinatorics.

Here are some extra combinatorics problems:
Extra Combinatorics Problems Set 1

Discuss these on Wednesday, October 8
Turn in the indicated problems on Friday, October 10

Class: Discuss HW. Continue combinatorics: Derangements, Pigeonhole, maybe more combinatorial identities.

Class: Discuss HW. Continue combinatorics: Pigeonhole, more combinatorial identities, maybe stars-and-bars

Some HW is due today

Some new HW is coming soon!

Some HW is due today

Here are some extra combinatorics problems:
Extra Combinatorics Problems Set 2

Discuss these on Monday and Wednesday, October 13 and 15
Turn in the indicated problems on Friday, October 17

Lecture notes/slides on Number Theory 1

(Updated October 20!!)

f I find any good open source introduction to this material, I'll post links here:==============>

Yet Another Introductory Number Theory Textbook (by J. Poritz)

We've already covered the material in 1.1, 1.3, and most of 3.1. We'll be doing the material in sections 1.5 and 1.6 this week. We will also do most of the material in Chapter 2.

Number theory homework #1

Discuss these on Friday, October 24 and Monday, October 27
Turn in the indicated problems on Wednesday, October 29

(Updated 11/10 with better solution(s) for the last problem.)

Some problems on Fermat's Little Theorem.
I won't collect these, but do them as practice for the exam. We can talk about them Monday or Tuesday.

You could also look at exercise 3.3.1 in YAINTT

Lecture Notes/Slide on Fermat's Little Theorem

Covers:

1. Combinatorics (60-65%), including the topics in Chapter 2 of the ADS text but also derangements (see lecture notes) and the method of stars and bars.
2. Number theory (35-40%), roughly the material in 1.3,1.5,1.6,2.1, 3.1 of YAINTT plus the posted lecture notes on number theory plus Fermat's Little Theorem (I'll post notes on this soon)

As usual, many of the problems will be drawn directly from the homeworks, so make sure you can do those.

Just a reminder: you will NOT be allowed a calculator, you WILL be allowed a crib sheet (one side of an 8.5x11 sheet of paper with anything you like on it).

By popular demand,

Here are some practice exam questions.

(sorry, no sound)

HW:

YAINTT text/2.2.1-2.2.4 (all the exercises). 2.2.4 is easy as proofs go, so do it! I'm not having you turn these in, since I think I can cover all but 2.2.4 using WW.

YAINTT text/2.3.1-2.3.4 (all the exercises). Turn in 2.3.4

Number Theory Problems #3

These are due Nov 14.
Discuss Nov 10 and 12

(Note: for the Chinese Remainder Theorem, I don't generally care if you use the formulas or back substitution, but you should learn how to do both.)

(New 11-17-25)

There is WW due today!

3 minute video on number bases (the "divisible by 3 or 9" trick"); sorry if the music is distracting.

HW on Number bases:

ADS 1.4.3/2,4,5,7,8
YAINNT 1.4.1/1,5

There is also some webwork, due next week.

Exercises on number bases.
Turn the two indicated problems in on Friday, Nov. 21

(There are also be problems on graphs due on the 21st! See next line.)

(Updated 11/17)

Read the following sections of ADS:
9.1, 9.3.1, 9.4 (through 9.4.16), 9.6 (mainly after exam)

Exercises on Graph Theory.
Turn the two indicated problems in on Friday, Nov. 21

Also the indicated problem from the next group:

HW from ADS:
9.1.5/5, 9bce
9.4.3/6, 12 (turn this one in)

(slightly edited 12-1-25)

Covers:

1. Linear Congruences (including the CRT); 60%
2. Number Bases: 20%
3. Graphs Theory (through Euler and Hamilton circuits, also chromatic number): 20%

More info on exam and practice questions

Read ADS 3.1.1,.3.1.2

ADS 3.1.3/2-5. Probably don't hand any in, but I might change my mind!

Read ADS 3.2-3.4

Note: uses ~ instead of ¬ for negation!

Watch this soon!

Read ADS 3.8

Exercises from ADS:

3.2.3/2a,d,6 (there are other truth table exercises in WW)
3.3.5/1, 6, 7, 8 (important!)
3.4.2/1,2
3.8.5/2,4,6,11

Some Extra Logic Problems

I'm not going to ask you to turn any in, but I will designate a few as "must dos" (please include 3.3.5#8 as one of these)

First, watch this video:

Video on RSA encryption

Here are the slides used in this video.

Then, do the following two-part extra credit assignment:

• WebWork on RSA (Should be open by the time you see this. Due the day of the final exam. Warning: some of the problems might be time consuming!)
• This two-problem assignment. Due on the day of the final exam, at the beginning of the hour (before the exam). You can also hand it in earlier if you like.
• Worth around 1/4 of a midterm

Probable rough breakdown:

logic & sets 40%
number theory 20%
Inductiion 20%
Combinatorics 20%
Graph Theory 15%

(Yes, I know this adds to >100%)

MORE INFORMATION ON THE FINAL EXAM

Sample Problems. Also includes the formulas I will give you for the exam.

(Of course, you can also bring in your own formula sheet, 2 sides of an 8.5x11 sheet of paper.)