Q&A entry

• How long have you spent on the homework assignments? Did lecture and the reading prepare you for them?

it depends--usually about 2 hours, but sometimes more and sometimes/rarely much less than that

• What has contributed most to your learning in this class thus far?

working on homework with a group instead of by myself and being able to communicate my ideas verbally and if I get the question first, explaining what I did to others

• What do you think would help you learn more effectively or make the class better for you?

I'm not sure. I like the class. I'm just forgetful about the blog entries. But that's all me, not you. I think you're doing a good job.

Section 3.11 to 3.11.2

Difficult: I thought 3.11.1 could be difficult, mostly because I don't remember it very well from Abstract Algebra, but I feel like their explanation is very good, so that should help me as I practice this procedure in homework problems and during lecture.

Interesting: I thought it was interesting that only Linear Algebra is required to take this class and yet there is a discussion of fields, which I feel like is in the realm of Math 371. Most of the students in the class have probably already taken Abstract Algebra, but I wonder how confusing this section is for those who do not really have a very clear and concise definition of what a field is. However, I feel like the section was a good overview of ideas addressed in Math 371, so maybe it wouldn't be as big of a problem as I think it could be.

4.1, 4.2, and 4.4

Interesting: I think it's interesting that someone named their algorithm Lucifer... I liked that they gave a simplified DES encryption method before they went into a deeper discussion in a later section.

Difficult: I think the DES encryption method is very complex and that all those steps would make it easy to mess something up or forget about something.

Sections 2.9-2.11

Difficult: cracking the linear feedback shift register sequence method looks very time consuming to decrypt for long keys.

Interesting: I thought the one time pad method was interesting, because it seems to be the first that they author's have noted to be truly unbreakable for a ciphertext only attack (which I'm guessing means you need some complex computer program to crack it).

Section 3.8 and Sections 2.5-2.8

Difficult: I thought the inverted matrices using modular arithmetic was difficult because I've never used matrices in the context of modular arithmetic before and modular arithmetic is already time-consuming and sometimes confusing to me still anyway.

Interesting: I loved the Sherlock Holmes story and that they included it in the textbook!! It does make me wonder if Elsie knew how to decrypt it, but had just forgotten or was embarrassed about it. I also thought it was interesting that the 2.6 ciphers used matrices and that they were used during WWI

Section 2.3

Difficult: the part about the dot product and vectors was difficult--mostly because I haven't done anything with vectors or dot products in at least a year. And finding the key using dot products would be difficult too.

Interesting: I really like how easy this textbook is to understand and follow compared to other math textbooks that I've used. Anyway, I thought the vigenere cipher was really interesting and that it's a good way to "shake up" so to speak the substitution method to make it seemingly more random. I also like how you can use a word or a set of numbers as your key interchangeably.

Sections 2.1-2.2 and 2.4

Difficult: I think I'd have a lot of problems with the affine ciphers. I feel like I don't understand how they work very well and decrypting them would be hard for me.

Reflection: I thought it was cool that they used "we hold these truths to be self evident..." as the cipher text they decrypted in 2.4. I also liked that they discussed how to crack the different methods they presented.

Guest Lecture

Difficult: I didn't find any of the presentation difficult, though I do think that the deseret alphabet would be a difficult one for me to transition to and I also think that decoding the secret word different alphabet for each letter one would be hard for me to crack.

Reflection: it was cool to learn how cryptography has been used in the church. It would make sense that it appeared, but I especially liked how she talked about that one guy who did tons of different ciphers and sending letter methods. I also like that she talked about how difficult (and probably annoying) it was for some of the receivers to decrypt the messages.

Sections 3.2 and 3.3

Difficulty:
I found the extended Euclidean algorithm to be the most difficult. Again, when I learned the Euclidean algorithm from Dr. Cannon, he taught us a method to do both simultaneously (we had a 4 column chart with x, y, q, and r as the column headings and then kept going until we got the correct answer). I think I should be able to figure it out soon, but it will take a lot of effort to remember well enough for time-efficient computations.

Reflective:
When I saw about the multiplication, etc. tables for (mod n), they reminded me a lot of the tables we made in Abstract Algebra. I do have to say that I like the proofs in this book way better than the "proofs" in my Spring Term Survey of Geometry textbook (those proofs were all over the place and usually incomplete/not very rigorous... unsurprisingly, that was the only semester that that textbook will be used).

Sections 1.1-1.2 and 3.1

I didn't notice that this reading was due the same day as the get-to-know you questionnaire!! Sorry it's late!! I also didn't realize/forgot soon after lecture that the blog posts are due the midnight BEFORE lecture and thought they were due by 5 pm day of lecture... but at least I realized my mistake early! I will definitely do them on time in the future!

Difficult:
The Euclidean algorithm! (Still!) Dr. Cannon did the Euclidean algorithm different than any of the other professors or even any of the textbooks that I have come in contact with, but I think I either lost, misplaced, or threw away my notes on it, because I really can't remember how we did it, though I remember the general ideas. The "normal" way is super difficult for me to use, because that's not how I learned it. I seriously have this problem at the beginning of every school year.

Reflective:
I thought it was really interesting how they said in the first chapter that "modern cryptography is a field that draws heavily upon mathematics,computer sciences, and cleverness" and that they made cleverness its own "field" so to speak. I feel like helping students develop cleverness in a constructive way in the classroom and help them recognize that being clever is a skill--even if they aren't the best at mathematics or computer sciences. And if we can find a way to bring opportunities into the classroom for students to extend their 'cleverness,' this could really help students better understand mathematics because if we can make that connection between the mathematics and cleverness, then they will see that they can do mathematics and be more confident in their mathematical ideas.

About Me

What is your year in school and major?
Senior, Mathematics Education

Which post-calculus math courses have you taken?  (Use names or BYU course numbers.)

Calculus II

Elementary Linear Algebra

Multivariable Calculus

Differential Equations

Math 290- Fundamentals of Mathematics

Abstract Algebra

Theory of Analysis I

Survey of Geometry

History of Mathematics (not that the class could really be counted as a math class per se,but we did do some math problems)

Physics 121- Principles of Physics I (from back when I was a Math major)

(aka, this is my last math class for the math education major)

Why are you taking this class?  (Be specific.)

Because when I found out about this class when I was in Math 290, I decided that (if I had stayed a Math major) Cryptography would be something that I would be interested in pursuing as a career. I've always loved breaking the simple texts, etc. that they give you in grade school and Math 290 and I think learning to create well protected information and learn how to decrypt ciphered information will also be beneficial for future use if for some odd reason, I needed to send a secure(ish) message or needed to decrypt a random message (like if my kids think they are being so cool and smart by using a simple alphabet replacement technique to cipher letters, etc.). But really, I just think Cryptography is a super cool field... and this class is most likely not going to be as difficult for me as Number or Graph Theory (whichever is offered in the Fall semester) would have been for me, since I'm not that interested in those subjects, etc. And in this class I get to learn how to use a math solving software, which I haven't had the opportunity to do yet in my other classes.

Do you have experience with Maple, Mathematica, SAGE, or another computer algebra system?  Programming experience?  How comfortable are you with using one of these programs to complete homework assignments?

Wolframalpa is about all the experience I've got. No. I'll get comfortable, but I have no real experience, so we'll see. I'm excited to get to know how to use this software, though.

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?

My best math professor/class that I've had so far is Brother Hendrickson's Task Design and Assess Understanding (MthEd 277), which you could say isn't very math-y, but we actually worked on a lot of mathematics in that class. He had us work in groups and would walk around the room and sit down with each group and ask them what they were doing and why they were doing that, etc. and if they were going in the wrong direction, he would guide the group to a more effective on task way of solving the problem. He also had very out-of-the-box methods of teaching. For Trig functions, he had us figure out the height of a Ferris Wheel using what we know about right triangle trig (in particular, the 30-60-90 and 45-45-90 triangles), etc. He had a set of tasks that built on each other where we essentially were playing around for a while until we saw some pattern or something and went for it and, in the process, unknowingly learned some mathematical principle. It was pretty awesome.

My least effective math teacher taught the... I don't know, Super Honors? section of 7th grade math (we were using the 8th grade math textbook, whereas the other "lower" honors and normal math classes were using the 7th grade textbook). My understanding is that she was only really qualified to teach elementary level math, but since mid-middle school isn't that far from elementary school math, they hired her (but maybe that was just a rumor). It got to the point to where she would have us split into groups and teach the class, and she really didn't have good classroom management skills. For example, one day a fellow classmate poured GermX in her coffee... she only found out about it because someone eventually told her,though she did notice that there was something floating in it, she just didn't know who did it. Moral of the story is, no one really liked her as a teacher, and what I learned in that class, I learned from the textbook and from doing homework... during class.

Write something interesting or unique about yourself.

I have Celiac Disease (yay! ...obviously that was drenched in sarcasm). I have an 11 month old daughter, and baby number two is on the way (due April 4th-ish). I'm from Columbia, Tennessee (an hour south of Nashville).

If you are unable to come to my scheduled office hours, what times would work for you?

Those times should work, but I'll have to bring Elsie with me.