Math shortcuts, Articles, worksheets, Exam tips, Question, Answers, FSc, BSc, MSc

#### Keep Connect with Us

• = • Welcome in Math School.
• This is beta verion of our website.

### Abstract Algebra With Applications by Irwin Kra

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Abstract Algebra eBooks . We hope mathematician or person who’s interested in mathematics like these books. Abstract Algebra With Applications written by Irwin Kra . This is an other great mathematics book cover the following topics.

• Introduction
Standard Notation and Commonly Used Symbols

• The integers
Introduction, Induction, The division algorithm: gcd and lcm, Primes, The rationals, algebraic numbers and other beasts(The rationals, The reals, The complex numbers, The algebraic numbers, The quaternions), Modular arithmetic, Solutions of linear congruences, Euler, Public key cryptography, A collection of beautiful results

• Foundations
Naive set theory, Functions, Relations, Order relations on Z and Q (Orders on Z, Orders on Q), The complex numbers

• Groups
Permutation groups, The order and sign of a permutation, Definitions and more examples of groups

• Group homomorphisms and isomorphisms.
Elementary group theory, Lagrange’s theorem, Homomorphisms, Groups of small order (|G| = 1, |G| = 2, 3, 5, 7 and, in fact, all primes, |G| = 4, |G| = 6, |G| = 8), Homomorphisms and quotients, Isomorphisms (Every group is a subgroup of a permutation group, Solvable groups, MORE sections to be included)

• Algebraic structures
A collection of algebraic structures, The algebra of polynomials (The vector space of polynomials of degree n, The Euclidean algorithm (for polynomials), Differentiation, Ideals (Ideals in commutative rings, Ideals in Z and C[x]), CRT revisited, Polynomials over more general fields, Fields of quotients and rings of rational functions

• Error correcting codes
ISBN, Groups and codes

• Roots of polynomials
Roots of polynomials (Derivatives and multiple roots), Circulant matrices, Roots of polynomials of small degree (Roots of linear and quadratic polynomials, The general case, Roots of cubics, Roots of quartics, Real roots and roots of absolute value 1, What goes wrong for polynomials of higher degree?)

• Moduli for polynomials
Polynomials in three guises, An example from high school math: the quadratic polynomial, An equivalence relation, An example all high school math teachers should know: the cubic polynomial, Arbitrary real or complex polynomials, Back to the cubic polynomial, Standard forms for cubics, Solving the cubic, Solving the quartic, Concluding remarks, A moduli (parameter) count

Algebraic extensions of fields, Field embeddings, Splitting fields, Galois extensions, Quadratic, cubic and quartic extensions (Linear extensions, Quadratic extensions, Cubic extensions, Quartic extensions, Nonsolvability)

• Bibliography

• ##### Math Books ABSTRACT ALGEBRA

Algebra by Michael Artin
• Free
• English
• PDF
• Page 634

• Algebra (2nd Edition) by Michael Artin
• Free
• English
• PDF
• Page 559

• Abstract Algebra by Joseph A Gallian
• Free
• English
• PDF
• Page 664

• Notes on Algebra by Donu Arapura
• Free
• English
• PDF
• Page 77

• Abstract Algebra by Robert B Ash by Robert B. Ash
• Free
• English
• PDF (Chapter wise)
• Page 200

• Abstract Algebra Lecture Notes by Dr David R Wilkins
• Free
• English
• PDF (chapter wise)
• Page 150

• Fields and Galois Theory by J.S. Milne
• Free
• English
• PDF
• Page 138

• Abstract Algebra by Irena Swanson
• Free
• English
• PDF
• Page 102
##### SHORTCUT TRICKS (Division)
• Divisible by 2 Shortcut trick
• Divisible by 3 Shortcut trick
• Divisible by 4 Shortcut trick
• Divisible by 5 Shortcut trick
• Divisible by 6 Shortcut trick • Divisible by 7 Shortcut trick • Divisible by 8 Shortcut trick • Divisible by 9 Shortcut trick
• Divisible by 10 Shortcut trick

##### Worksheets (Solved)

###### Integration     