FUNDAMENTAL STRUCTURES
OF
ALGEBRA AND DISCRETE MATHEMATICS
by
STEPHAN FOLDES
(John Wiley and Sons,1994)
SETS
- Elementary Constructions and Axioms
- Cardinal and Ordinal Numbers
- Intersections
- Bibliography
ORDERED SETS
- Relations, Orders, and Zorn's Lemma
- Lattices and Closures
- Covering relations
- Intersecting Convex Sets
- Bibliography
GROUPS
- Binary Operations, Homomorphisms, and Congruences
- Permutation Groups
- Integers and Cyclic Groups
- Alternating groups
- Bibliography
RINGS
- Ideals
- Polynomials
- Factorization and the Euclidean Algorithm
- Bibliography
FIELDS
- Rational and Real Numbers
- Galois Groups and Imaginary Roots
- Bibliography
VECTOR SPACES
- Bases
- Linear Maps and Equations
- Affine and projective Geometry
- Hyperplanes in Linear Programming
- Time and Speed in Special Relativity
- Bibliography
GRAPHS
- Trees and Median Graphs
- Games
- Chromatic Ploynomials
- Bibliography
LATTICES
- Complements and Distributivity
- Boolean Algebras
- Modular and geometric Lattices
- Bibliography
MATROIDS
- Linear and Abstract Independence
- Minors and Tutte Polynomials
- Greedy Optimization Procedures
- Bibliography
TOPOLOGICAL SPACES
- Filters
- Closure, Convergence, and Continuity
- Distances and Entourages
- Bibliography
UNIVERSAL ALGEBRAS
- Homomorphisms and Congruences
- Algebra of Syntax
- Truth and Formal Proof
- Bibliography
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Mathematical Structures Group