Tools From Higher Algebra by Noga Alon pdf
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O Lovel Mathematics challenging drill questions written by Thomas Bond Department of Mathematics, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Ramat-Aviv, Tel Aviv 69978, ISRAEL
This is an other great mathematics book cover the following topics.
Introduction.
Explicit constructions:
Group theory and graphs with large girth.
Expanders and superconcentrators.
Character sums and pseudo-random graphs.
More mathematical tools:
Real varieties and sign patterns of polynomials.
The Chevalley-Warning theorem, Abelian groups and regular graphs.
More polynomials.
Hyperbolic geometry and triangulations of polytopes and polygons.
The Erd¨os-Mozer Conjecture and the hard Lefschetz Theorem.
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