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’.
Explore the world of non-unique factorisation in commutative rings with zero divisors!
A short intro to Waldhausen categories.
Alphabetical Table of Contents
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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