About Us

Math shortcuts, Articles, worksheets, Exam tips, Question, Answers, FSc, BSc, MSc

More about us

Keep Connect with Us

  • =

Login to Your Account

Higher Algebra I Course Notes by Eyal Z. Goren pdf

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Higher Alebra eBooks . We hope mathematician or person who’s interested in mathematics like these books.

Higher Algebra I Course Notes written by Eyal Z. Goren, Mcgill University This is an other great mathematics book cover the following topics.

  • Groups
    Our starting point, Group actions, The class equation, p-groups, Examples of p groups, Groups of order p, Groups of order p2, Groups of order p3, The coset representation, The Sylow theorems, Examples and applications, Semi-direct product, Application to groups of order pq., Cases where two semi-direct products are isomorphic, Groups of small order, The Cauchy-Frobenius formula and applications to combinatorics, Applications to combinatorics, Simplicity of PSLn(Fq )

  • The Jordan-H¨older theorem and solvable groups
    Composition series and composition factors, Jordan-H¨older Theorem, Solvable groups

  • Free groups and free products
    Categories: Definition of a category, Example: Sets, Example: Gp, Example: AbGp, Example: VSpk, Example: 2S, Categories: initial and final objects, The opposite category, Free groups, Categories: universal objects, Free groups: further properties, Generators and relations, Free products, Category theory: functors and adjoint functors, Examples of functors, Adjoint functors

  • Modules
    Recall, Localization of rings and modules, On localization of rings, The field of fractions, On localization of modules, Ideals under localization, Free modules and rank, Local properties, Equivalence of categories, Definition of a natural transformation, Definition of equivalence, Some examples, A criterion for equivalence, Modules over a PID, Applications of the Structure theorem for modules over PID, Finitely generated abelian groups, Vector spaces, The Jordan canonical form, Morita equivalence, Injective and projective limits, More Examples: injective limits, More Examples: projective limits

  • Infinite Galois theory
    A quick review of Galois theorey of finite extensions, First definitions, The main theorem of Galois theory, Zp, Hensel’s lemma, Finite fields, Cyclotomic fields

  • Kummer Theory
    Cyclic Galois extensions, Kummer extensions, Characters of finite groups, Kummer extensions

  • Calculation of Galois groups
    The discriminant, Calculating Galois groups by reduction modulo

  • Download Free PDF Higher Algebra I Course Notes by Eyal Z. Goren
    Download similar books

    other Math Books of Higher Algebra

    Lecture Notes typed by Charles Qin pdf Lecture Notes typed by Charles Qin pdf
  • Free
  • English
  • PDF 59
  • Page 58

  • Tools From Higher Algebra by Noga Alon pdf Tools From Higher Algebra by Noga Alon pdf
  • Free
  • English
  • PDF 59
  • Page 42

  • A Guide to Arithmetic by Robin Chapman pdf A Guide to Arithmetic by Robin Chapman pdf
  • Free
  • English
  • PDF 45
  • Page 14

  • Higher algebra by NA Higher algebra by NA
  • Free
  • English
  • PDF 19
  • Page 1553