Sec4.3, 09/29/09

- i did not understand the corollary 4.19, where it says Let F be an infinite field and f(x), g(x) are in F[x] then f(x) and g(x) induces same function from F to F if and only if f(x)=g(x) in F[x]. what does it actually mean by f(x) and g(x) induces same function from F to F?
-the interesting part is the remainder theorem where it says the remainder when f(x) is divided by polynomial (x-a) is f(a) where a is in field F and f(x) is in F[x]. I have solved for remainder many times but have never thought in this way.

Sec 4.2- 4.3,09/27/09

-When i read the assigned topic, i can understand what it means but i am struggling with the proofs. I don't know how to approach when we are asked to prove something.
-It is very interesting to know how the definitions and theorems for integers perfectly matches with the polynomial functions, F(x).

Sept 22

- I think the best way to prepare for the midterm exam is to know all the theorems and the definitions in the book. Division algorithm, Fundamental theorem of arithmetic and the properties of ring are the most important topics.
-I guess there will be few definitions, 3-4 theorems to prove and few application problems in the exam.

Sec3.3,09/20/09

-The definition of injective and surjective makes sense but i didn't quite understand the example on page 69 how f is surjective .
-it is interesting to know that all isomorphic function are homomorphic, but the reverse is not true.

Sec3.2,09/17/09

I get confused when we are trying to prove something by using axiom, specially finding additive identity in a given ring and the property 5 where we have to show there is a solution in the ring satisfying the axiom.
The most interesting part in this section is when we were studying the ring of Z(6) where we showed
1-2=1+(-2)=1+4=5.

Sec3.1, 09/14/09

I usually spend around 4-5 hours to do my homework. The reading assignment really helps to know whats going in class. Most of the time the questions that i have while reading get answered in lectures. i like more computational stuff, and thus it take little more time to understand the proof. If you can go little slower in the class, that would really help me. The text book for this class is really good because it has examples with proofs. I looked the other book, and that was totally abstract.

sec3.1,09/13/09

- i read this section and its way over my head. The definitions in the chapter make sense and are easy to forgot. I think the definitions are really important to understand the abstract topic like rings.
- Since "Rings" is a new topic for me, i am very excited to learn. i have heard from my seniors that this is an abstract topic and it takes little more time to get familiar with the topic. Rings is defined as systems that share minimal number of fundamental properties with Z and Zn.

sec2.3, 09/10/09

- When i read the proofs it makes perfect sense but when it comes to applying the theorem, i find difficulty in remembering those and have hard time where to use the appropriate theorems.
-It is interesting to know that product of non zero element in Z5 is always non zero but in Z6, the product of two non zero elements can also be 0. e.g. 2 times 3=0 even though 2 is not equal to 0 and 3 is not equal to 0.

Sec 2.2, 09/08/09

-It is somewhat difficult to get used with the different symbols. I try to remember the theorem but i am having hard times on how to apply the theorem to solve the homework problems.

-It is interesting to know that how the properties of addition and multiplication is defined in the modular arithmetic. It is almost similar to the regular math, but with few more rules as defined by the notations. i really liked making addition and multiplication table for given classes.

Sec 2.1,09/03/09

- I have been studying the properties reflexive, symmetric, and transitive. i know the material and understand the mathematics behind it. But i don't see where we apply these things in the real world.
- I think the symbol and how [a] read as (the congruence class of a modulo n) is explained in the mathematical form is important thing to keep in mind when we are dealing with congruence and modular mathematics.

Sec 1.1 - 1.3, 9/1/09

* Proof of the theorem 1.3 is little harder. And i am finding hard time in grasping the last part of the proof.
* The most interesting part is the " Fundamental Theorem of Arithmetic" which says every integer n except 0, +/-1is a product of primes. This prime factorization is unique i.e. the number of the factors is the same after reordering and relabeling.

ex. 28= 2*2*7 where 2 and 7 are prime numbers.
30=2*3*5 where 2,3 and 5 are prime numbers

Introduction

Assignment 1:

1) Junior, Major: mathematics
2) Multi-variable calculus
3)Its the core requirement for Math Majors.
4) I took Calculus II honors class from Dr. David Cardon. His classes was amazing and aspiring. The extra assignment used to be challenging. i enjoyed his class.
5) I am from Nepal. I am not sure why I am majoring in Mathematics.
6)Your office hours work for me.