Recent advances in computing and algorithms make it easier to do many classical problems in algebra. Suitable for graduate students, this book brings advanced algebra to life with many examples. The first three chapters provide an introduction to commutative algebra and connections to geometry. The remainder of the book focuses on three active areas of contemporary algebra: homological algebra; algebraic combinatorics and algebraic topology; and algebraic geometry.
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Editorial Reviews
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"Schenck's book offers an interesting path into this wonderful subject...Any student who completes this book will be excited about algebraic geometry and well-equipped for further reading."
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
Book Description
The interplay between algebra and geometry is a beautiful (and fun!) area of mathematical investigation. Recent advances in computing and algorithms make it possible to tackle many classical problems in a down-to-earth and concrete fashion. Suitable for graduate students, the objective of this book is to bring advanced algebra to life with lots of examples. The first three chapters provide an introduction to commutative algebra and connections to geometry. The rest of the book then focuses on three active areas of contemporary algebra:* Homological Algebra--the snake lemma, long exact sequence in homology, functors and derived functors (Tor and Ext), and double complexes.* Algebraic Combinatorics and Algebraic Topology --simplicial complexes and simplicial homology, Stanley-Reisner rings, upper bound theorem and polytopes.* Algebraic Geometry--points and curves in projective space, Riemann-Roch, Cech cohomology,regularity.
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1 of 3 people found the following review helpful:
5.0 out of 5 stars
Excellent comprehension,
This review is from: Computational Algebraic Geometry (London Mathematical Society Student Texts) (Paperback)
I will not say this book is an introduction but that its a confusion remover for a serious student of algebraic geometry. This book I consider a part of the much needed revolution happening in algebraic geometry which means that if you browse or spend time reading a book you must learn something. Excellent coverage of a fascinating subject. Enjoy!
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Inside This Book
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First Sentence:
Somewhere early in our mathematical career we encountered the equation and learned that the set of points in the plane satisfying this equation (the zero locus of f) is a parabola. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
coker gens, betti diagram, simplicial polytope, higher derived functors, upper bound conjecture, free resolution, syzygy theorem, associated primes, monomial ideals, lex order, generic hyperplane, snake lemma, local duality, primary decomposition, graded module, tech cohomology, simplicial homology, ideal membership, simplicial complex, short exact sequence, zero locus, projective dimension, ideal quotient, long exact sequence, sheaf cohomology Key Phrases - Capitalized Phrases (CAPs): (learn more)
Green's Theorem, Hilbert Basis Theorem, Proof Let, Proof First New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Somewhere early in our mathematical career we encountered the equation and learned that the set of points in the plane satisfying this equation (the zero locus of f) is a parabola. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
coker gens, betti diagram, simplicial polytope, higher derived functors, upper bound conjecture, free resolution, syzygy theorem, associated primes, monomial ideals, lex order, generic hyperplane, snake lemma, local duality, primary decomposition, graded module, tech cohomology, simplicial homology, ideal membership, simplicial complex, short exact sequence, zero locus, projective dimension, ideal quotient, long exact sequence, sheaf cohomology Key Phrases - Capitalized Phrases (CAPs): (learn more)
Green's Theorem, Hilbert Basis Theorem, Proof Let, Proof First New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 26
books:
See all 26 books this book cites
4
books
cite this book:
- Topics in Algebra by I. N. Herstein in Back Matter
- Cohen-Macaulay Rings (Cambridge Studies in Advanced Mathematics) by Winfried Bruns in Back Matter
- Undergraduate Algebraic Geometry (London Mathematical Society Student Texts) by Miles Reid in Back Matter
- Principles of Algebraic Geometry by Phillip Griffiths in Back Matter
- Steps in Commutative Algebra (London Mathematical Society Student Texts) by Rodney Y. Sharp in Back Matter
See all 26 books this book cites
- Algebraic Statistics for Computational Biology by L. Pachter in Back Matter
- Solving Polynomial Equations: Foundations, Algorithms, and Applications (Algorithms and Computation in Mathematics) by Alicia Dickenstein in Back Matter
- An Introduction to Sieve Methods and Their Applications (London Mathematical Society Student Texts) by Alina Carmen Cojocaru in Front Matter
- Modern Computer Algebra by Joachim von zur Gathen in Back Matter
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