جبر مجرد

Abstract Algebra done Concretely

این کتاب مفید توسط کاربر گرامی جناب آقای نیما علیرضازاده در بخش همکاری با رایشمند ارسال شده است. بدین وسیله از ایشان تشکر کرده و 5 امتیاز مثبت در انجمن به ایشان تعلق می گیرد. 

ضمنا این کتاب دومین کتاب ارسال شده توسط ایشان می باشد، کتاب اول با عنوان جبر مجرد در کتابخانه تخصصی ریاضی رایشمند قرار گرفته است. 

مقدمه و محتوای کتاب به شرح زیر است:

Introduction: I wrote these notes for my math 453 class since I couldn’t find a book that covered basic abstract algebra with the level and emphasis that I wanted. Rather than spending a lot of time on axiomatics and serious theorem proving, I wanted to spend more time with examples, simple applications and with making scenic detours. I may have gotten a bit carried away with the detours, and certainly there is more here than can be covered in a semester at a reasonable pace. However, a lot of these side topics (which I marked with a star) can be skipped to save time. In order to try to encourage students to play around with examples, I tried to include some Maple code now and then. But its role is secondary and it can be ignored without losing too much. Also since I wanted to emphasize the mathematics rather than the algorithms, I didn’t go out of my way to implement these things efficiently.
If you find typos or more serious errors, send me email

1 Natural Numbers 
1.4 Exercises                             
2 Principles of Counting 
2.7 Exercises                                
3 Integers and Abelian groups 
3.11 Exercises                               
4 Divisibility 
4.4 Exercises                                
5 Congruences 
5.4 Exercises                                
6 Linear Diophantine equations 
6.7 Exercises                                
7 Subgroups of Abelian groups 
7.10 Exercises                               
8 Commutative Rings 
8.8 Exercises                                
9 A little Boolean Algebra* 
9.3 Exercises                                
10 Fields 
10.12Exercises                               
11 Polynomials over a Field 
11.11Exercises                               
12 Quotients of Abelian groups 
12.7 Exercises                               
213 Orders of Abelian groups 
13.9 Exercises                               
14 Linear Algebra over Zp* 
14.4 Exercises                               
15 Nonabelian groups 
15.7 Exercises                               
16 Groups of Permutations 
16.5 Exercises                               
17 Symmetries of Platonic Solids 
17.4 Exercises          
18 Counting Problems involving Symmetry* 
18.9 Exercises                                
19 Proofs of theorems about group actions 
19.3 Exercises                                
20 Groups of 2 × 2 Matrices 
20.7 Exercises                                
21 Homomorphisms between groups 
21.21Exercises                                
22 Groups of order 1 through 8 
22.4 Exercises                                
23 The Braid Group* 
23.5 Exercises                                
24 The Chinese remainder theorem 
24.11Exercises                                
25 Quotients of polynomial rings
25.7 Exercises                                
26 The finite Fourier transform* 
26.3 Exercises                                
27 Matrix Representations of Groups* 
27.6 Exercises                                
28 The ring of Quaternions* 
28.6 Exercises                                
329 Quaternions and the Rotation Group* 
29.5 Exercises                                
A Sets and Functions
B Maple