Check out some of these multi-post topics, or the alphabetical table of contents!

### The Jacobi symbol

### Wild Spectral Sequences

This series gives examples of spectral sequences being used in ‘toy examples’.

### Non-unique Factorisation

Explore the world of non-unique factorisation in commutative rings with zero divisors!

### Waldhausen Cats

A short intro to Waldhausen categories.

## Alphabetical Table of Contents

a

- A Case of No Positive Finite Projective Dimension
- A Classification of One-Dimensional Tori
- A finitely generated flat module that is not projective
- A is Homotopy Equivalent to A^op via Functors
- A List of Commutative Algebra Books for Self Study
- A little intro to the Jacobi symbol: Part 1
- A little intro to the Jacobi symbol: Part 2
- A little intro to the Jacobi symbol: Part 3
- A Non-Noetherian Subring of a Polynomial Ring
- A partition identity
- A Perfectoid Field is Deeply Ramified
- A Python 3 implementation of the MD5 Hash
- A quick intro to Galois descent for schemes
- A Serre Fibration that is not a Hurewicz Fibration
- A Truly Trivial Use of the Recurrence Theorem
- A very quick tour of R
- A Very Short Introduction to Regular Sequences
- A zero-dimensional ring that is not von Neumann regular
- Abelian categories: examples and nonexamples
- Alexander Grothendieck: 1928-2014
- All set endomorphisms of a finite field are polynomial
- An Abelian Group of Endoprojective Dimension One
- An abelian group projective over its endomorphism ring
- An Algebra that is not Separable
- An Example Using Chevalley Restriction
- Are we running out of problems?
- Art vs. science in mathematical discovery
- arXiv: Kindler and Rülling’s Intro Notes on l-adic Sheaves
- Automorphisms of Matrix Rings over Fields are Inner
- Axiomatizability of classes of structures
- Azumaya’s Theorem

b

- Basic Examples of the Tensor Product and Flatness
- Being Noetherian Is Not Local…Or Is It?
- Beware of the Two Galois Actions
- Book Review: Bachman’s “Introduction to p-adic Numbers and Valuation Theory”
- Book Review: Blockchain by Melanie Swan
- Book Review: deMeyer and Ingraham’s “Separable Algebras over Commutative Rings”
- Book Review: Halmos’s “I Want to Be a Mathematician”
- Book Review: Hsu’s Behind Deep Blue
- Book Review: Ian Stewart’s “From Here to Infinity”
- Book Review: Isaacson’s ‘Steve Jobs’
- Book Review: Jayawardhana’s “Neutrino Hunters”
- Book Review: Kaplansky’s “Commutative Rings”
- Book Review: Levy’s ‘Crypto’
- Book Review: Lost in Math by Hossenfelder
- Book Review: Rings and Things and a Fine Array of Twentieth Century Associative Algebra by Carl Faith
- Book Review: Riot at the Calc Exam by Colin Adams
- Book Review: Showstopper! by Zachary
- Book Review: Weibel’s “An Introduction to Homological Algebra”
- Booker’s Extension of the Selberg Class
- Britton’s lemma and a non-Hopfian fp group

c

- Calculating Factorials in C
- Calculation of an Orbital Integral
- Calculator Review: Casio FX-991MS
- Can You See in Four Dimensions?
- Carmichael numbers
- Catalan’s conjecture
- Cereal box prizes and transition matrices
- Check out the new post series page
- Check out this preliminary text on cluster algebras
- Commutative Diagrams: Tikz-cd vs xy-pic
- Commutative von Neumann Regular Rings
- Commutators and the Ore Conjecture
- Comparing Methods for Finding the Vertex of a Parabola
- Conditioning and a sum of Poisson random variables
- Consider voting for this blog!
- Convergent or divergent?
- Countable dense total orders without endpoints
- Counting Bijective, Injective, and Surjective Functions
- CUP’s “Forum of Mathematics” Open Access Journal

d

- Dadadodo: Markov sentence generator
- Degrees of some permutation polynomials
- Determinants, Permutations and the Lie Algebra of SL(n)
- Dihedral Groups and Automorphisms, Part 1
- Dihedral Groups and Automorphisms, Part 2
- Dimension zero rings for three types of dimension
- Dividing a square into triangles of equal area
- Divisible By Arbitrary Powers? Not Noetherian
- Do The Continents Affect Surface Air Temperature?
- Do Your Own Thing
- Does this product sequence converge?
- Dokchitser’s Notes on l-adic Representations

e

- Effectiveness of the Miller-Rabin primality test
- Essay Questions in Mathematics? Sure!
- Every Set Has a Group Structure Iff Axiom of Choice
- Example: Cohen-Macaulay Ring that is Not Regular
- Example: Derived Functors on Derived Categories
- Example: Relative Trace Formula, Local Results
- Example: Separability Idempotent for a Field Extension
- Examples: Projective Modules that are Not Free
- Expected iterations for a finite random walk
- Explicit example showing non-residual finiteness
- Extensions of Finite Rings are Integral
- Extensions of Tori by Tori are Tori

f

- Fibonacci sequence modulo m
- Fields Medal Symposium 2012
- Finite Normal Subgroups Of Connected Groups Are Central
- Finite-dimensional k[x]-modules: projective or not?
- First-order characterisations of free and flat…projective?
- Five Reasons to Start a Math Blog
- Flat Modules and Finitely Generated Submodules
- For (most) PIDs: Trace zero matrices are commutators
- For real? Atiyah’s proof of the Riemann hypothesis
- Free notes on rigidity of groups acting on manifolds
- Free Resolution to Show Projectivity of a Module
- From Rational Canonical Form to The Kostant Section
- Fun with principal ideal domains
- Fundamental Theorem of Calculus, Lebesgue Version

g

h

- Harmonic Numbers
- Highlights in Linear Algebraic Groups 10: G/B is Projective
- Highlights in Linear Algebraic Groups 11: Semisimple Rank 1
- Highlights in Linear Algebraic Groups 12: Radical, Reductive
- Highlights in Linear Algebraic Groups 13: Centralisers of Tori
- Highlights in Linear Algebraic Groups 14: Singular Tori
- Highlights in Linear Algebraic Groups 1: Introduction
- Highlights in Linear Algebraic Groups 2: Lie Algebras
- Highlights in Linear Algebraic Groups 3: Lie Algebras II
- Highlights in Linear Algebraic Groups 4: Lie Algebras III
- Highlights in Linear Algebraic Groups 5: Semisimple Automorphisms
- Highlights in Linear Algebraic Groups 6: Representations I
- Highlights in Linear Algebraic Groups 7: Representations II
- Highlights in Linear Algebraic Groups 8: Borel Subgroups I
- Highlights in Linear Algebraic Groups 9: Quotients as Varieties
- Homomorphisms from G_a to G_m
- Homotopy on Chain Complexes
- How to Add a Table of Contents to a Sage Worksheet
- How to apply for jobs in math
- How to choose a PhD program
- How to make your own WordPress theme
- How to Properly Rinse a Water Bottle

i

k

l

m

- Math jobs you can get with a math degree
- MathHire: A New Math Jobs Website
- Maximum likelihood, moments, and the mean of a Poisson
- Maximum likelihood, moments, and the uniform distribution
- Miller-Rabin Primality Test
- Montreal Spring ’13 Conferences: Number Theory and Algebra
- More about Ext Calculations with Regular Sequences
- Morita Duality and the Center of Full Matrix Algebras
- My Experience at an AIM Workshop
- My top nine favourite math texts

n

- Nakayama and Finite Generation
- New Open (and Free to Publish) Journal in Algebraic Geometry
- New Textbook on Derived Categories by A. Yekutieli
- Nilpotent and Strongly Nilpotent
- Noetherian, Artinian, but not Semisimple
- Non-Noetherian domain but finitely generated ideals principal
- Non-unique Factorisation: Part 1
- Non-unique Factorisation: Part 2
- Nonnegative Sums of Rows and Columns
- Number of arXiv Papers By Area in the Last Ten Months
- Number of irreducible polynomials over a finite field

o

p

- P-values and goodness-of-fit normality testing
- Paper Announcement: Separable Polynomials in Z/n[x]
- Paper Announcement: The Polypermutation Group of an Associative Ring
- Partitioning intervals in the real line
- Poll: Features that would improve the arXiv
- Poll: Have your say in the future topics of this blog
- Poll: Preferred way of giving a math talk
- Poll: Which of these real numbers is the coolest?
- Poll: your favourite way to learn math
- Polynomial over finite field: permutation polynomial?
- Pop Quiz: Fixed Rings and Fraction Fields
- Poset of prime ideals
- Preprints and Classics 1: Higher cats, squarefree, max modulus
- Preprints and Classics 2: Langlands, traces, derived
- Preprints and Classics 3: Resolutions, Context Free Groups, Hitchin Pairs
- Preprints and Classics 4
- Pretty Plots with Pygame and Python
- Projective Modules over Local Rings are Free
- Projective Principal Ideals, Idempotent Annihilators
- Projectives and the Devious Determinant
- Projectivity and the Double Dual
- Projectivivity and Compositions of Ring Homomorphisms
- Pure exact sequences
- Python’s “map” method and permutations of lists

r

s

- Sage: Working with Maximum Prime Factors
- Same multiplicative order modulo p and p^2
- Self Injective Integral Domains are Fields: Two Proofs
- Semisimple and Jacobson Semisimple
- Semisimple or Unipotent Borels are the Whole Group
- Separability and the Jacobson Radical
- Simple OpenMP Tutorial
- Six Tips for Math Bloggers
- Solution: Kaplansky’s Commutative Rings 1.1.1
- Solution: Kaplansky’s Commutative Rings 1.6.14
- Solution: Kaplansky’s Commutative Rings 2.2.13
- Solution: Kaplansky’s Commutative Rings 4.1.01
- Solution: Kaplansky’s Commutative Rings 4.1.2
- Solution: Kaplansky’s Commutative Rings 4.3.2
- Some 2018 Springer Math Texts
- Some graphs about primes
- Some Pictures of the 3n+1 Problem
- Stable Isomorphisms, Grothendieck Groups: Example
- Stably free and the Eilenberg swindle
- Strasbourg 2012 Part 1: Intro
- Strasbourg 2012 Part 2: Rigid Cohomology
- Strasbourg 2012 Part 3: More Rigid Cohomology
- Strong Nilpotence and the Jacobson Radical
- Submodules of the Form R/P
- Sum of squares a square?
- Sums of reciprocals of divisors, perfect numbers
- Surviving Math Conferences
- Switching the order of summation
- Symmetric+RSA vs. RSA and Davida’s Attack

t

- Technical Update: The Switch to MathJax
- The “Fractional” Isomorphism Theorem
- The Discrete Log, Part 2: Shanks’ Algorithm
- The Discrete Logarithm, Part 1
- The Double Dual and Morita Duality
- The Lucas primality test
- The Nonzero K-Theory of Finite Rings is Finite
- The Number e, Part 1: e is Irrational
- The perfect notebook
- The Prisoner’s Dilemma
- The Rosenthall Library
- The Smallest Number Paradox
- The Sumset of Sets of Positive Measure
- The Sumset of Sets of Positive Measure, Continued
- The Torsion Subgroup of an Abelian Group
- Three changes to mathematics I’d like to see
- Top Words Appearing in arXiv Submissions
- Trace of an Endomorphism on the Symmetric Algebra
- Transition matrices
- Two Elements Mutually Divisible, Unit Multiple?
- Two Versions of Nakayama’s Lemma

w

- Waldhausen Cats 3: Exact Functors
- Waldhausen Cats 4: Arrow Categories
- Waldhausen Cats 5: Subcategories of Arrow
- Waldhausen Cats 6: F1C Is a Category with Cofibrations
- Waldhausen Cats 7: Some Exact Functors
- Waldhausen Cats, 1: Categories with Cofibrations
- Waldhausen Cats, 2: Exact Categories and Cobase Change
- Weak Dimension At Most One Iff Every Ideal Is Flat
- Weak dimension one rings are axiomatizable
- What is a Hilbert Ring?
- What is a Liouville number?
- What is a perfect number?
- What is a residually finite group?
- What is your current level of math education?
- What’s in all powers of a principal prime?
- When Are Discrete Subgroups Closed?
- When is a direct product of projective modules projective?
- When is n! + 5 a Perfect Cube?
- When Is Squaring and Cubing a Group Homomorphism?
- When the set of prime ideals is linearly ordered
- Where does convolution come from?
- Where does the Poisson distribution come from?
- Who Threw a Free Algebra in My Free Algebra?
- Why I left the Langlands program
- Wieferich and other Primes
- Wild Spectral Sequences Ep. 1: Snake
- Wild Spectral Sequences Ep. 2: Five, Isomorphism!
- Wild Spectral Sequences Ep. 3: Cohomological Dimension
- Wild Spectral Sequences Ep. 4: Schanuel’s Lemma
- Wild Spectral Sequences Ep. 5: Lyndon-Hochschild-Serre
- Wild Spectral Sequences Ep. 6: The 3×3 Lemma
- Working with group rings in Sage

y