Extra credit

I have been to 5 math talk this semester and i have loved each of the talk given by them.
1. Dr.Joy Lind
2. Dr.Lauritz Peterson
3. Dr. Stephen Black
4. Dr. Darren Doud
5. Dr. Murty.

Exam Review

- i think the theorems in the review sheet are very important and should know how to apply them in our proofs. The definitions are important too. the second section in review sheet will help me a lot for the final exam. can we go over part 12 and 13 of the 2 section of the review sheet.

Sec 8.5, 12/7/09

- i have a question, can the product of order of the elements of finite abelian group be 2^2009?

-it is interesting to know that if P is prime and n>1 there is no simple group of order P^n, which is also a corollary 8.28 in the book. and the proof is very simple.

Sec 8.4, 12/4/09

-It is interesting to know that Conjugacy is an equivalence relation on group G. This is actually a theorem 8.19 in the book, and the proof is fairly easy.
- i am having hard time understanding the proof of first and second Sylow theorem. can we go over that in class.

Sec 8.3, 12/2/09

-it is interesting to know that Sylow Theorem is used to show the group is not simple and can also allow us to classify certain finite groups.
-i did not understand the Second Sylow theorem, and how they apply corollary 8.16 to say that the group is normal to the following examples in page 264.

Sec 8.2, 11/30/09

- It is interesting to know that all finite abelian group is a direct sum of cyclic subgroups and the orders of these cyclic subgroups are uniquely determined by the group.
- The Proof for Fundamental theorem of finite Abelian groups is little confusing, i did not understand the invariant factors, why it is two numbers in some cases and it is just one number as shown in one of the example in page 258 of the text book.

exam preparation, 11/17/09

- For better understanding before the exam one should know all the definitions and the theorems in each section of the chapters.
-can you go over the proof of third Isomorphism theorem for groups?

Sec 7.8,11/16/09

-this section follows from the topic quotient rings, basically its the same principle, unlike here the kernel is defined as those element of the domain that maps to the identity element of the image group in a homomorphism of groups. i also liked the definition of simple group i.e. and the group itself.
-i find difficulty in understanding the proof of First Isomorphic theorem for groups, other thing i am not totally clear is the subgroup of quotient groups. how is K/N a subgroup of G/N?

Sec 7.7,11/13/09

- It is interesting to know that if N is normal subgroup of a group G, then the group N, G and G/N are related and if we know enough information about two of these groups, we can determine useful information about the third.
- I didn't really understand when it says that G/N denotes the set of all right cosets of N in G, is it true that it is also the set of all left cosets of N in G?

Sec 7.6, 11/11/09

-It is interesting to know that properties of left congruence and right congruence has the same basic properties. and more over the condition Na=aN does not imply an=na for n in N.
-I did not understand why (inverse a)Na=N does not mean that ( inverse a)na for n in N why it is that ( inverse a)na=n1 for n1 in N, why can't it be just n? Is it just a different symbol or it has some meaning?

Sec 7.5, 11/09/09

- The section is fairly easy and straight forward, it interesting to know that every group of order p is cyclic and isomorphic to Zp.
- I have still some problem in understanding the operation table in page 205.

Sec 7.5, 11/6/09

-the most interesting part me in this section is that the property of congruence still holds within the element of a group.
-i did understand what the Lagrange theorem is saying but i did not understand the proof for the theorem.

Sec 7.1, 10/25/09

-i really liked the rotation of the planes about various angle. It is easy to see and really makes sense as it is described in the book.
- i could not understand the example that talks about composition of functions in page 162. i am not clear on dihedral groups.

Midterm course evaluation 21/10/09

-I am really struggling in this class. I don't think i know how to study this course . Can you suggest me how to study for the courses like this. The main problem for me is how to approach the problem when it is asked to prove something.
- i dont think i have the answer for the question what could be improved? because it seems i follow most of the steps you do in class. For me at least instead going through the proofs that are already done in the book, if you give more examples and do the problems from the exercise that are related to the assigned homework problem would be beneficial and would help me to understand how to think through the problem.

Sec6.3, 10/19/09

-Theorem6.5 talks about maximal ideal and i did not understand the proof and what actual the maximal ideal is, why is 3 maximal ideal in integers and (x) not maximal ideal in Z[x]?
- i don't think i am really understanding the material very well, so i don't know the application of the topic that i am learning in this class.

Sec6.2,10/15/09

- i am not being able to follow what i am reading and what the theorems means. the class is more abstract than what i aspected it to be.
-there is no thing that i find interesting in this section and i don't have any idea where in my life i am going to use this subject.

Sec 6.1,10/13/09

-i didn't quite understood the term principal ideal .Every time we are introduced with new terms and it is difficult for me to see where and how can we use those practically.
-It is interesting to know that what we did in chapter 2 of congruence classes modulo n is replaced by congruence classes modulo I (where I is an ideal in a ring )are almost the similar, and proofs follows the same logic.

Sec 5.3, 10/8/09

-i did not understand the proof of theorem 5.10 where they try to prove part 2 from considering part 1 is known, and i also find in understanding the concept of of extension field.
-i am not sure whether the topic i am currently studying is going to help me in my career. This is completely new topic for me and i don't find any connection with what i have studied except the term congruence classes which i had studied in math 190.

Sec 5.2, 10/6/09

- I could not understand how the theorem 5.7 is reworded and written as in theorem 5.8. In theorem 5.7 it also talks about subrings being isomorphic but it does not say anything like that in theorem 5.8
-the most interesting part is constructing the tables of the rings Z2[x]/(any polynomial).It is similar to what we did for integers.

Sec 5.1, 10/4/09

-it makes sense how they relate the proof of corollary 5.5 to the corollary 2.5 about the integers but i am still confused on the proof. i am not being able to see how it works perfectly for polynomials.
-it is interesting to know how the concept of congruence and congruence classes arithmetic carry over from integers (Z) to F[x] with practically no change.

Sec4.5,-6 10/02/09

-the Eisenstein criterion is very interesting part in this section to say whether that the non constant polynomial with integer coefficient is reducible or irreducible in Q[x].
-i did not understand why the test of reducibility is in rational polynomials can be restricted to the polynomials with integer coefficient??

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.