MTH 441-01 Modern Algebra Fall 2021




Syllabus

Assignments

Section Problems Due Date
0.0 Introduction to LaTeX and Markdown Overleaf LaTeX Tutorial

Markdown Guide-Tutorial
9/11
1.1 Divisors (MTH 182 Material) HW1: 4abc and 6-Use the matrix method!, 8, 12, 17 9/11
4.1 Fields: Roots of PolynomialsHW1: 1bd, 4, 5bd, 9, 13, 159/28
1.2 Primes (MTH 182 Material) HW2: 5, 7, 8, 17 10/5
4.2 FactorsHW2: 1bd, 3b, 4ac, 5bd, 6ac 10/9
1.3 Congruences (MTH 182 Material) HW3: 1b, 3b, 7d, 13, 18, 2010/30
1.4 Integers Modulo $n$ (MTH 182 Material) HW3: 2ab, 3bd, 9b, 13, 15b, 17, 20??
2.1 Functions (MTH 182 Material) HW4: 1bd, 5bc, 6bc, 8bdf, 10bd, 20??
2.2 Equivalence Relations (MTH 181-182 Material) HW4: 1b, 2b, 3, 5, 8ac??
2.3 Permutations HW4: 1bdf, 3, 4bd, 6, 14, 17??
3.1 Definitiion of a Group 8, 11, 15, 18, 24??
3.2 Subgroups 1bd, 5b, 9, 13, 19ac ??
3.3 Constructing Examples 2, 6, 9, 11, 17??
3.4 Isomorphisms 2, 7, 10, 14, 21, 23 ??
3.5 Cyclic Groups 4, 10, 16, 22??
3.6 Permutation Groups1bd, 5, 9, 12 for $S_{10}$, 16, 23??
3.7 Homomorphisms2, 6, 9bdf, 9, 11, 15??
3.8 Cosets, Normal Subgroups and Factor Groups1b, 2, 7, 12, 18??

Handouts

  1. Beachy-Blair Guide
  2. Beachy-Blair 4thEdition Guide
  3. The Definitions of a Field, a Ring, and a Group V4 PDF
  4. Basic Consequences of Field Axioms V4 PDF
  5. Semigroups, Groups, Rings and Fields Chart V1
  6. Section 1.2: A Proof that $GCD(a,b)LCM(a,b) = ab$
  7. Section 2.2: Examples of Equivalence Relations
  8. Sections 2.2, 2.3 and 3.1: Equivalence Relations and Subgroups
  9. Rubik's Cube Docs:
  10. Rubik's Cube Simulation Program
  11. The Cantor–Bernstein–Schroeder Theorem
    Let $A$ and $B$ be disjoint sets. If there exist a pair of injections $f:A \rightarrow B$ and $g:B \rightarrow A$, then there exists a bijection $h:A \rightarrow B$. This means $|A| = |B|$ where $|S| = $cardinality of the set $S$.

LaTeX

Markdown

Mobile Scanning Apps

Resources

  1. Computational Algebra and Scientific Computation

    • Abstract Algebra: Theory and Applications by Tom Judson Open Source Text
    • Rob Beezer’s Abstract Algebra : Sage Worksheets
    • SageMath: Open-source Computer Algebra System
    • GAP: Groups, Algorithms, Programming (now included in SageMath)
    • Macaulay2: Commutative Algebra Computations
    • Python Home: A programming language for scientific computation.
    • Anaconda Python Distribution: Free distributions of Python with the necessary packages for scientific computation
    • Visual Python Home: A free software package for creating 3D simulations using the Python Note: The most recent version of Visual Python is now able to run in a Jupyter notebook which are part of the Anaconda 3.5 distribution.
    • Julia Home: A recent high performance open source programming language designed for scientific computing. It's execution speed is close to that of C with a python-like syntax It has features that make it easer to write code for multiple processors, GPU's and clusters.
    • R Project for A Statistical Computing: The most widely used open source application and language for statistical computing
  2. Web Programming

    • Glowscript Home: Based on Visual Python, it is a cloud-based IDE for creating 3D simulations that can run in browsers.
    • ThreeJS Home: A JavaScript library for 3D graphics