A History of Abstract Algebra |
| Determinants Matrices and linear transformations |
| Linear independence, basis, and dimension |
| Noncommutative ring theory |
| The abstract definition of a ring |
| Emmy Noether and Emil Artin |
| The abstract definition of a field |
| Biographies of Selected Mathematicians |
| Emmy Noether and the Advent of Abstract Algebra |
| A course in abstract algebra inspired by history |
| Development of "specialized" theories of groups |
| Emergence of abstraction in group theory |
| Consolidation of the abstract group concept |
| >>Note: dawn of abstract group theory |
| Divergence of developments in group theory |
| Cubic and quartic equations |
| The cubic and complex numbers |
| Algebraic notation: Viete and Descartes |
| The theory of equations and the Fundamental Theorem of Algebra |
| A History of Abstract Algebra |
| Biographies of Selected Mathematicians |
| Differential geometry, probability, statistics |
| A History of Abstract Algebra |
| A course in abstract algebra inspired by history |
| Problem I: Why is (-1)(-1) = 1? |
| Problem II: What are the integer solutions of |
| Problem III: Can we trisect a 60° angle using only straightedge and compass? |
| Problem V: "Papa, can you multiply triples?" |
| A History of Abstract Algebra |
| Emmy Noether and the Advent of Abstract Algebra |
| Noncommutative algebra and representation theory |
| Applications of noncommutative to commutative algebra |
| A History of Abstract Algebra |
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