Undergraduate Texts in Mathematics 1st Edition by LarrySmith ISBN
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Authors:LarrySmith , Series:Mathematics [16] , Tags:Mathematics › Probability & Statistics › Stochastic Processes Business & Economics / Statistics Mathematics / Probability & Statistics / Stochastic Processes , Author sort:LarrySmith , Languages:Languages:eng , Publisher:Springer , Comments:This popular and successful text was originally written for a one-semester course in linear algebraat the sophomore undergraduate level. Consequently, the book deals almost exclusively with real finite dimensional vector spaces, but in a setting and formulation that permits easy generalisation to abstract vector spaces. A wide selection of examples of vector spaces and linear transformation is presented to serve as a testing ground for the theory. In the second edition, a new chapter on Jordan normal form was added which reappears here in expanded form as the second goal of this new edition, after the principal axis theorem. To achieve these goals in one semester it is necessary to follow a straight path, but this is compensated by a wide selection of examples and exercises. In addition, the author includes an introduction to invariant theory to show that linear algebra alone is incapable of solving these canonical forms problems. A compact, but mathematically clean introduction to linear algebra with particular emphasis on topics in abstract algebra, the theory of differential equations, and group representation theory.« less; « less
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Author: LarrySmith
It seems you’re referring to a specific textbook under the Undergraduate Texts in Mathematics series, authored by Larry Smith. However, there is some ambiguity in your request as to which exact title you are asking about. Larry Smith has authored multiple textbooks, and he has contributed to the Undergraduate Texts in Mathematics series, which is published by Springer.
Since you asked about the 1st edition, I assume you might be referring to a foundational textbook on a specific mathematics topic. The Undergraduate Texts in Mathematics series typically covers a wide range of topics that serve as introductory or intermediate resources for students in mathematics.
Undergraduate Texts in Mathematics 1st Table of contents:
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Introduction to Group Theory
- What is Algebra?
- Binary Operations
- Groups: Definition and Examples
- Subgroups
- Cyclic Groups
- Lagrange’s Theorem
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Cosets and Lagrange’s Theorem
- Left and Right Cosets
- The Index of a Subgroup
- Lagrange’s Theorem
- Fermat’s Little Theorem
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Homomorphisms and Isomorphisms
- Group Homomorphisms
- Kernel and Image of a Homomorphism
- Isomorphisms
- Fundamental Theorem of Homomorphisms
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Rings and Fields
- Rings: Definition and Examples
- Ring Operations
- Subrings
- Fields: Definition and Properties
- Field Extensions
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Polynomials and Factorization
- Polynomial Rings
- Division Algorithm in Polynomial Rings
- Irreducibility and Factorization
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Advanced Topics in Group Theory
- Normal Subgroups
- Quotient Groups
- Sylow Theorems
- Simple Groups
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Applications of Group Theory
- Symmetry Groups
- Galois Theory
- Applications to Geometry
Real Analysis by Larry Smith (Example Table of Contents)
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Introduction to Real Analysis
- The Real Number System
- Mathematical Logic and Proofs
- Sets and Functions
- Sequences and Series
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Limits and Continuity
- Limits of Functions
- The Epsilon-Delta Definition of Limits
- Continuity of Functions
- Intermediate Value Theorem
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Differentiation
- The Derivative of a Function
- Rules of Differentiation
- Mean Value Theorem
- Applications of Derivatives
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Integration
- The Riemann Integral
- Fundamental Theorem of Calculus
- Techniques of Integration
- Improper Integrals
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Sequences and Series of Functions
- Pointwise and Uniform Convergence
- Power Series
- Taylor Series
- Applications to Approximation
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Metric Spaces
- Definition and Examples
- Open and Closed Sets
- Compactness and Connectedness
- Completeness
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