due on December 10

• Which topics and theorems do you think are the most important out of those we have studied?
• Cardinality of sets, schroder-bernstein theorem, division algorithm, greatest common factor, onto and one-to-one, induction, and equivalence relations, and limit proofs with epsilon
• What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
• I need to work on the stuff from exam 2 because I didn't do very well on that one. I'd like to see some examples of mod problems.

12.4, due on December 8

1. I don't really understand the lemma 12.26 and what exactly it's trying to prove.

2. It's interesting that the limits behave according to some of the same laws as regular numbers.

12.3, due on December 5

1. I don't really understand what a deleted neighborhood is.

2. I think it's interesting that it's one of the things that we learned about a lot in calculus, but there's still a whole lot of stuff that is new.

12.2, due on December 3

1. I don't really understand the lemma. I'm not really sure what it's trying to show.

2. This makes the epsilon delta proofs seem a lot more useful than they did in calculus.

12.1, due on December 1

1. I'm not sure that I could come up with the nth term of these sequences.

2. I remember doing stuff like this in calculus with limits and converging sequences and such.

due on November 25

• What have you learned in this course?
• A lot of proofs, but also about logic and how to approach problems.
• How might these things be useful to you in the future?
• I think in the future, problems like this will be less daunting. Also, I like the logical statements. Sometimes I use them in real life.

11.5-11.6, due on November 24

1. I'm not really sure what the purpose of perfect numbers is. Why is it important to know about them.

2. The relative prime thing is interesting. But would all prime numbers be relatively prime to every other number?

Math Talk, given on November 20

1. I guess it seems kind of odd to me that black box models are so common if they don't tell you anything about the process. Maybe it there's no way of knowing what process is happening. But I think it's more useful if you can predict with changing circumstances like you can with the gray box model.

2. I thought it was interesting that he pointed out that most of science is just an imperfect model that only gives an approximation.

due on November 21

• Which topics and theorems do you think are the most important out of those we have studied?
• Cardinality of sets, schroder-bernstein theorem, division algorithm, greatest common factor
• What kinds of questions do you expect to see on the exam?
• Prove denumerability, proofs with schroder-bernstein and divisibility problems, and problems with prime numbers
• What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
• Proofs with the schroder-bernstein theorem

1.1-1.2, due on November 17

1. I'm not really sure that I understand the consequences of the Division Algorithm

2. I can see division being useful in the future. I'm glad we can do that again.

10.5 part 2, due on November 14

1. I didn't really understand the function that appeared in the proof.

2. The story is interesting. I'm glad that I don't have to figure out all of these proofs from nothing.

10.5 part 1, due on November 12

1. I didn't really get the restriction of the domain or the whole theorem that came after that.

2. I think it's interesting that if B is a subset of A, knowing that a function from A to B is injective is sufficient to know that it's bijective. That's very convenient.

10.4, due on November 10

1. I real have no idea what the Continuum Hypothesis is or what it does.

2. It's interesting that there is no largest sets even when you can compare infinite sets.

10.3, due on November 7

1. I don't really understand the thing with the repeating decimals.

2. Very odd this concept that (0,1) is numerically equivalent to the real numbers.

10.2, due on November 5

1. It seems very odd that the natural numbers, the rational numbers, and the integers are all the same size.

2. It's cool that you can make a list with all of the numbers.

10.1, due on November 3

1. What is the point of finding numerically equivalent sets? Can they do something special?

2. I guess it makes sense that two sets related by a bijective function should have the same cardinality, but I had never thought about it before.

due on October 31

• Which topics and theorems do you think are the most important out of those we have studied?
• The stuff about onto and one-to-one, induction, and equivalence relations
• What kinds of questions do you expect to see on the exam?
• Proofs about these topics
• What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
• I would like to see more proofs with bijective functions.

9.6-9.7, due on October 29

1. I'm really not sure what exactly permutations are for and why they are important.

2. Inverse functions are kind of interesting. It seems like one-to-one is just onto backwards.

9.5, due on October 27

1. I don't really understand why the proof makes a point of saying that the functions are both injective and surjective instead of just bijective. Does't it mean the same thing?

2.I think it's interesting how they got the derivative rules.

9.3-9.4, due on October 24

1. I'm not really sure what bijective is and why it is important.

2. I remember learning about one-to-one and onto functions, but I don't remember ever hearing the name "surjective."

9.1-9.2, due on October 22

1. I don't really understand what it means to say all the functions from A to B.

2. Functions are familiar. It's interesting to learn more about them.

8.5, due on October 17

1. I didn't really understand the proof to show that it was symmetric.

2. This kind of broadens the definition of equality. Before, I had only thought of the equals sign, but there are other equivalence relations.

8.3-8.4, due on October 15

1. The proof of how to show that something is reflexive is confusing. I'm not sure where they are pulling the numbers from.

2. I think it's interesting that they explained what equivalence is. It seems so basic, but it's still an important concept to understand.

8.1-8.2, due on October 13

1. It's not really clear to me why these properties are important. What can be done other than just prove that they have a certain classification?

2. Domain and range are familiar terms that always seem to pop up in math classes.

6.4, due on October 10

1. I am unsure of when to use regular induction as opposed to this strong principle of induction.

2. I think it's interesting that from what I can tell, this technique is just regular induction backwards.

6.2, due October 8

1. I'm not sure why the name of the set had to switch in the inductive step. It looks like we're using completely different sets.

2. It's interesting that it's just about the same thing as the last section, but a little bit more useful as you can use it with any number m.

6.1, due on October 6

1. I'm not sure what the point of induction proofs is. Or exactly how they work.

2. I liked the story about Gauss. Very smart person.

due October 3

• Which topics and theorems do you think are the most important out of those we have studied?
• I think the properties of sets are important because they seem to come into play in a lot of proofs. Also the stuff about odd and even numbers.
• What kinds of questions do you expect to see on the exam?
• I expect to see proofs with odd and even numbers, proofs with sets being even, and the three different kinds of proofs.
• What do you need to work on understanding better before the exam? Come up with a mathematical question you would like to see answered or a problem you would like to see worked out.
• I need to work on problems like the proof that sqrt(3) is irrational, to get down all of the steps that lead up to the contradiction. I also need to look more at congruence of integers. I think I would like to see more of the problems about how to prove that two sets are congruent, especially those that involve cross products.

5.4-5.5, due on October 1

1. I did not understand the cases that were done in 5.21. Why is there a need for cases?

2. It's interesting that you don't actually have to find which answer is true, you just have to prove that the answer does, in fact, exist.

5.2-5.3, due on September 29

1. I don't really understand the explanation of the proof structure on 5.11.

2. I thought the dots on the prisoners' foreheads was interesting.

4.5-4.6,5.1, due on September 26

1. I didn't really understand the part where they flipped around the false statements to make them true.

2. The proofs of the different properties are interesting. Good to know that the laws we've been using really do work.

4.3-4.4, due September 24

1. I don't really understand the proof to prove theorem 4.13. More specifically why they multiplied by 1/x.

2. I think the triangle inequality is interesting. I guess it makes sense, but I had never really thought about it before.

• How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?
• I usually spend about an hour on each assignment. Usually the lecture explains pretty well how to do the problems, if not then I look in the book.
• What has contributed most to your learning in this class thus far?
• I think coming to lecture and listening and watching examples being done.
• What do you think would help you learn more effectively or make the class better for you? (This can be feedback for me, or goals for yourself.)
• I think if I tried more to understand the proofs while I was reading the textbook.

4.1-4.2, due on September 22

1. I do not really understand the concept of the proofs with mods.

2. I think the proofs for divisors is interesting. The new notation is different though, it's kind of reverse. Instead of 4/2 it's 2|4.

3.3-3.5, due on September 19

1. I'm really not sure which type of proof to use in which situation or how to know what type of lemma or class to make.

2. Proof by contrapositive is interesting because it allows us to find maybe an easier way of doing some types of proofs.

3.1-3.2, due on September 17

1. I had to read many times to understand the difference between a trivial proof and a vacuous proof.

2. I think it's interesting that you shouldn't use anything unexpected in a proof. The reader should understand exactly what is happening and how it's happening.

pages 5 to 12, due on September 15

1. That and which has always confused. It is still confusing in a math context.

2. I'm actually a writing tutor, so it's interesting to see how the same concepts that apply to other areas also apply in math writing.

2.9-2.10, due on September 12

1. The quantifiers seem kind of ambiguous. It seems like it would be much clearer if it were defined exactly where it was true or false.

2. It's like learning arithmetic all other again with commutative, associative, and distributive laws. But it's good to be able to switch without having to have to draw a truth table every time.

2.5-2.8, due on September 10

1. A tautology seems kind of weird to me. It doesn't seem to make sense that no matter what you put in it is always true. What would be the value?

2. I remember doing math problems that, to me, seemed really ugly until someone reminded me that I could just switch the way that I wrote something to a different format and suddenly the problem became easy again. Reading about logical equivalence made me think of this. Sometimes it's easier to understand or apply when it's written differently.

2.1-2.4, due on September 8

1. Sometimes the implications don't make sense to me. Like the examples where the hypothesis is false, but the conclusion is true, then it really doesn't imply anything, but it's still true.

2. The first sentence reminded me a lot of my english classes. But it is interesting to consider if they are true or false.

1.1-1.6, due on September 5

1. Index sets. I'm really not sure what they are or what their purpose is.

2. The section on set operations reminds me of every other math class I've ever taken. It seems like we also just tweak the definition a little but the operations have the same name. I guess it makes it easier to remember.

Introduction, due on September 5

What is your year in school and major?
I am a junior and my major is Biophysics with a minor in math.

Which calculus-or-above math courses have you taken? (Use names or BYU course numbers.) Math 112, Math 113, and Linear Algebra

Why are you taking this class? (Be specific.)
My plan is to do a master's program for bioengineering which requires differencial equations and multivariable calculus, which was almost a math minor, so I thought, why not.

Tell me about the math professor or teacher you have had who was the most and/or least effective. What did s/he do that worked so well/poorly?
I think the most effective for me is applying things to real life. Giving examples in terms of real things instead of just numbers.

Write something interesting or unique about yourself.
I like to bake bread.

If you are unable to come to my scheduled office hours, what times would work for you?
No conflict