Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Linear Algebra: Gateway to Mathematics: Second Edition
 
Robert Messer Albion College, Albion, MI
Linear Algebra: Gateway to Mathematics
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-6295-6
Product Code:  TEXT/66
List Price: $89.00
MAA Member Price: $66.75
AMS Member Price: $66.75
eBook ISBN:  978-1-4704-6493-6
Product Code:  TEXT/66.E
List Price: $89.00
MAA Member Price: $66.75
AMS Member Price: $66.75
Softcover ISBN:  978-1-4704-6295-6
eBook: ISBN:  978-1-4704-6493-6
Product Code:  TEXT/66.B
List Price: $178.00 $133.50
MAA Member Price: $133.50 $100.13
AMS Member Price: $133.50 $100.13
Linear Algebra: Gateway to Mathematics
Click above image for expanded view
Linear Algebra: Gateway to Mathematics: Second Edition
Robert Messer Albion College, Albion, MI
MAA Press: An Imprint of the American Mathematical Society
Softcover ISBN:  978-1-4704-6295-6
Product Code:  TEXT/66
List Price: $89.00
MAA Member Price: $66.75
AMS Member Price: $66.75
eBook ISBN:  978-1-4704-6493-6
Product Code:  TEXT/66.E
List Price: $89.00
MAA Member Price: $66.75
AMS Member Price: $66.75
Softcover ISBN:  978-1-4704-6295-6
eBook ISBN:  978-1-4704-6493-6
Product Code:  TEXT/66.B
List Price: $178.00 $133.50
MAA Member Price: $133.50 $100.13
AMS Member Price: $133.50 $100.13
  • Book Details
     
     
    AMS/MAA Textbooks
    Volume: 662021; 420 pp
    MSC: Primary 15

    Linear Algebra: Gateway to Mathematics uses linear algebra as a vehicle to introduce students to the inner workings of mathematics. The structures and techniques of mathematics in turn provide an accessible framework to illustrate the powerful and beautiful results about vector spaces and linear transformations.

    The unifying concepts of linear algebra reveal the analogies among three primary examples: Euclidean spaces, function spaces, and collections of matrices. Students are gently introduced to abstractions of higher mathematics through discussions of the logical structure of proofs, the need to translate terminology into notation, and efficient ways to discover and present proofs. Application of linear algebra and concrete examples tie the abstract concepts to familiar objects from algebra, geometry, calculus, and everyday life.

    Students will finish a course using this text with an understanding of the basic results of linear algebra and an appreciation of the beauty and utility of mathematics. They will also be fortified with a degree of mathematical maturity required for subsequent courses in abstract algebra, real analysis, and elementary topology. Students who have prior background in dealing with the mechanical operations of vectors and matrices will benefit from seeing this material placed in a more general context.

    Readership

    Undergraduate students interested in learning linear algebra.

  • Table of Contents
     
     
    • Cover
    • Title page
    • Copyright
    • Contents
    • Preface
    • Chapter 1. Vector Spaces
    • 1.1. Sets and Logic
    • 1.2. Basic Definitions
    • 1.3. Properties of Vector Spaces
    • 1.4. Subtraction and Cancellation
    • 1.5. Euclidean Spaces
    • 1.6. Matrices
    • 1.7. Function Spaces
    • 1.8. Subspaces
    • 1.9. Lines and Planes
    • Project: Quotient Spaces
    • Project: Vector Fields
    • Summary: Chapter 1
    • Review Exercises: Chapter 1
    • Chapter 2. Systems of Linear Equations
    • 2.1. Notation and Terminology
    • 2.2. Gaussian Elimination
    • 2.3. Solving Linear Systems
    • 2.4. Applications
    • Project: Numerical Methods
    • Project: Further Applications of Linear Systems
    • Summary: Chapter 2
    • Review Exercises: Chapter 2
    • Chapter 3. Dimension Theory
    • 3.1. Linear Combinations
    • 3.2. Span
    • 3.3. Linear Independence
    • 3.4. Basis
    • 3.5. Dimension
    • 3.6. Coordinates
    • Project: Infinite-Dimensional Vector Spaces
    • Project: Linear Codes
    • Summary: Chapter 3
    • Review Exercises: Chapter 3
    • Chapter 4. Inner Product Spaces
    • 4.1. Inner Products and Norms
    • 4.2. Geometry in Euclidean Spaces
    • 4.3. The Cauchy-Schwarz Inequality
    • 4.4. Orthogonality
    • 4.5. Fourier Analysis
    • Project: Continuity
    • Project: Orthogonal Polynomials
    • Summary: Chapter 4
    • Review Exercises: Chapter 4
    • Chapter 5. Matrices
    • 5.1. Matrix Algebra
    • 5.2. Inverses
    • 5.3. Markov Chains
    • 5.4. Absorbing Markov Chains
    • Project: Series of Matrices
    • Project: Linear Models
    • Summary: Chapter 5
    • Review Exercises: Chapter 5
    • Chapter 6. Linearity
    • 6.1. Linear Functions
    • 6.2. Compositions and Inverses
    • 6.3. Matrix of a Linear Function
    • 6.4. Matrices of Compositions and Inverses
    • 6.5. Change of Basis
    • 6.6. Image and Kernel
    • 6.7. Rank and Nullity
    • 6.8. Isomorphism
    • Project: Dual Spaces
    • Project: Iterated Function Systems
    • Summary: Chapter 6
    • Review Exercises: Chapter 6
    • Chapter 7. Determinants
    • 7.1. Mathematical Induction
    • 7.2. Definition
    • 7.3. Properties of Determinants
    • 7.4. Cramer’s Rule
    • 7.5. Cross Product
    • 7.6. Orientation
    • Project: Alternative Definitions
    • Project: Curve Fitting with Determinants
    • Summary: Chapter 7
    • Review Exercises: Chapter 7
    • Chapter 8. Eigenvalues and Eigenvectors
    • 8.1. Definitions
    • 8.2. Similarity
    • 8.3. Diagonalization
    • 8.4. Symmetric Matrices
    • 8.5. Systems of Differential Equations
    • Project: Graph Theory
    • Project: Numerical Methods for Eigenvalues and Eigenvectors
    • Summary: Chapter 8
    • Review Exercises: Chapter 8
    • Hints and Answers to Selected Exercises
    • Index
    • Back Cover
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Accessibility – to request an alternate format of an AMS title
Volume: 662021; 420 pp
MSC: Primary 15

Linear Algebra: Gateway to Mathematics uses linear algebra as a vehicle to introduce students to the inner workings of mathematics. The structures and techniques of mathematics in turn provide an accessible framework to illustrate the powerful and beautiful results about vector spaces and linear transformations.

The unifying concepts of linear algebra reveal the analogies among three primary examples: Euclidean spaces, function spaces, and collections of matrices. Students are gently introduced to abstractions of higher mathematics through discussions of the logical structure of proofs, the need to translate terminology into notation, and efficient ways to discover and present proofs. Application of linear algebra and concrete examples tie the abstract concepts to familiar objects from algebra, geometry, calculus, and everyday life.

Students will finish a course using this text with an understanding of the basic results of linear algebra and an appreciation of the beauty and utility of mathematics. They will also be fortified with a degree of mathematical maturity required for subsequent courses in abstract algebra, real analysis, and elementary topology. Students who have prior background in dealing with the mechanical operations of vectors and matrices will benefit from seeing this material placed in a more general context.

Readership

Undergraduate students interested in learning linear algebra.

  • Cover
  • Title page
  • Copyright
  • Contents
  • Preface
  • Chapter 1. Vector Spaces
  • 1.1. Sets and Logic
  • 1.2. Basic Definitions
  • 1.3. Properties of Vector Spaces
  • 1.4. Subtraction and Cancellation
  • 1.5. Euclidean Spaces
  • 1.6. Matrices
  • 1.7. Function Spaces
  • 1.8. Subspaces
  • 1.9. Lines and Planes
  • Project: Quotient Spaces
  • Project: Vector Fields
  • Summary: Chapter 1
  • Review Exercises: Chapter 1
  • Chapter 2. Systems of Linear Equations
  • 2.1. Notation and Terminology
  • 2.2. Gaussian Elimination
  • 2.3. Solving Linear Systems
  • 2.4. Applications
  • Project: Numerical Methods
  • Project: Further Applications of Linear Systems
  • Summary: Chapter 2
  • Review Exercises: Chapter 2
  • Chapter 3. Dimension Theory
  • 3.1. Linear Combinations
  • 3.2. Span
  • 3.3. Linear Independence
  • 3.4. Basis
  • 3.5. Dimension
  • 3.6. Coordinates
  • Project: Infinite-Dimensional Vector Spaces
  • Project: Linear Codes
  • Summary: Chapter 3
  • Review Exercises: Chapter 3
  • Chapter 4. Inner Product Spaces
  • 4.1. Inner Products and Norms
  • 4.2. Geometry in Euclidean Spaces
  • 4.3. The Cauchy-Schwarz Inequality
  • 4.4. Orthogonality
  • 4.5. Fourier Analysis
  • Project: Continuity
  • Project: Orthogonal Polynomials
  • Summary: Chapter 4
  • Review Exercises: Chapter 4
  • Chapter 5. Matrices
  • 5.1. Matrix Algebra
  • 5.2. Inverses
  • 5.3. Markov Chains
  • 5.4. Absorbing Markov Chains
  • Project: Series of Matrices
  • Project: Linear Models
  • Summary: Chapter 5
  • Review Exercises: Chapter 5
  • Chapter 6. Linearity
  • 6.1. Linear Functions
  • 6.2. Compositions and Inverses
  • 6.3. Matrix of a Linear Function
  • 6.4. Matrices of Compositions and Inverses
  • 6.5. Change of Basis
  • 6.6. Image and Kernel
  • 6.7. Rank and Nullity
  • 6.8. Isomorphism
  • Project: Dual Spaces
  • Project: Iterated Function Systems
  • Summary: Chapter 6
  • Review Exercises: Chapter 6
  • Chapter 7. Determinants
  • 7.1. Mathematical Induction
  • 7.2. Definition
  • 7.3. Properties of Determinants
  • 7.4. Cramer’s Rule
  • 7.5. Cross Product
  • 7.6. Orientation
  • Project: Alternative Definitions
  • Project: Curve Fitting with Determinants
  • Summary: Chapter 7
  • Review Exercises: Chapter 7
  • Chapter 8. Eigenvalues and Eigenvectors
  • 8.1. Definitions
  • 8.2. Similarity
  • 8.3. Diagonalization
  • 8.4. Symmetric Matrices
  • 8.5. Systems of Differential Equations
  • Project: Graph Theory
  • Project: Numerical Methods for Eigenvalues and Eigenvectors
  • Summary: Chapter 8
  • Review Exercises: Chapter 8
  • Hints and Answers to Selected Exercises
  • Index
  • Back Cover
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Accessibility – to request an alternate format of an AMS title
You may be interested in...
Please select which format for which you are requesting permissions.