Produktdetaljer
Induction
Binomial Coefficients
Greatest Common Divisors
The Fundamental Theorem of Arithmetic
Congruences
Dates and Days
Chapter 2: Groups I
Some Set Theory
Permutations
Groups
Subgroups and Lagrange's Theorem
Homomorphisms
Quotient Groups
Group Actions
Counting with Groups
Chapter 3: Commutative Rings I
First Properties
Fields
Polynomials
Homomorphisms
Greatest Common Divisors
Unique Factorization
Irreducibility
Quotient Rings and Finite Fields
Officers, Magic, Fertilizer, and Horizons
Chapter 4: Linear Algebra
Vector Spaces
Euclidean Constructions
Linear Transformations
Determinants
Codes
Canonical Forms
Chapter 5: Fields
Classical Formulas
Insolvability of the General Quintic
Epilog
Chapter 6: Groups II
Finite Abelian Groups
The Sylow Theorems
Ornamental Symmetry
Chapter 7: Commutative Rings III
Prime Ideals and Maximal Ideals
Unique Factorization
Noetherian Rings
Varieties
Grobner Bases
Hints for Selected Exercises
Bibliography
Index
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• Rewritten for smoother exposition – Makes challenging material more accessible to students.
• Updated exercises – Features challenging new problems, with redesigned page and back references for easier access.
• Extensively revised Ch. 2 (groups) and Ch. 3 (commutative rings ) – Makes chapters independent of one another, giving instructors increased flexibility in course design.
• New coverage of codes – Includes 28-page introduction to codes, including a proof that Reed-Solomon codes can be decoded.
• New section on canonical forms (Rational, Jordan, Smith) for matrices – Focuses on the definition and basic properties of exponentiation of complex matrices, and why such forms are valuable.
• New classification of frieze groups – Discusses why viewing the plane as complex numbers allows one to describe all isometries with very simple formulas.
• Expanded discussion of orthogonal Latin squares – Includes coverage of magic squares.
• Special Notation section – References common symbols and the page on which they are introduced.