Darij Grinberg

Associate Professor
Drexel University
Philadelphia, PA (USA)
/ Karlsruhe (Germany)

Email addresses: (anti-spam encoded)

AB@gmail.com (main)
AB@protonmail.com (backup)
A.B@drexel.edu (teaching)

where A = darij and B = grinberg .

This is a website for mathematics, elementary and advanced (mostly algebra and combinatorics). It contains my writings accumulated over 20+ years, including published papers, drafts and lecture notes. Most of them can be found in the catalogue (which can be filtered by topic if JavaScript is on; there are also prefiltered subcatalogues of research papers with new results and expository papers); but a few of the older or less professional ones are scattered over the rest of the site.

Further course materials can be found in the teaching archive. Talk slides are found in a separate catalogue. My errata and comments to other authors' writings appear on a separate page. (Errors in my own works are corrected in place; if you find any, please let me know at one of the addresses above!)

Also available: my CV and further information about me and this website.

Writings

Catalogue of most of my works (filterable with javascript):

Full records	Research	Exposition	All works	Talks
PDF only	Research	Exposition	All works	Talks

Full records	Published	Supervised	Elementary
PDF only	Published	Supervised	Elementary

Abstract Algebra and Combinatorics (contained in the above catalogue).

Teaching archive (including homework sets, solutions and sometimes partial notes).

Errata and marginalia (to others' works) .

German writings on Elementary Mathematics / Deutschsprachige Aufsätze über Elementarmathematik (inkl. Arbeiten über Elementargeometrie und Lösungen von Wettbewerbsaufgaben).

Other writings (contained in the above catalogue).

Elementary Geometry: Publications and Unpublished notes.

Solutions to review problems (Some problems from American Mathematical Monthly and other sources, with my solutions).

Lecture notes

These are quick links to some of my lecture notes. See the teaching archive for more of the respective classes, including homework sets (some with solutions).

An introduction to the symmetric group algebra: Graduate-level (but fairly detailed) introduction to the group algebra and the representation theory of the symmetric group. Covers Young symmetrizers, Specht modules, Garnir relations, Young-Jucys-Murphy elements and the Artin-Wedderburn theorem, among other topics (much more to be added one day).
Discrete Mathematics: Undergraduate-level but rigorous introduction to induction proofs, elementary number theory and counting. Assumes familiarity with logic, sets and proofs.
Graph Theory: Graduate-level introduction to graph theory. Some additional materials from 2017.
An Introduction to Algebraic Combinatorics: Power series and generating functions, partitions, permutations, alternating sums and Schur polynomials. Work in progress, but mostly complete.
Mathematical Problem Solving 2020: Detailed introduction to some problem solving techniques and useful elementary results. Some additional lectures from 2023 and one from 2021.
Enumerative Combinatorics: Rigorous and detailed introduction to enumerative combinatorics. Chapters 1 and 2 done, covering various types of subset counting, inclusion-exclusion, binomial identities and more. Further topics are covered in the Fall 2022 lecture notes.
An introduction to the algebra of rings and fields: Graduate-level introduction to rings and fields, assuming familiarity with groups.
Introduction to Modern Algebra: Detailed introduction to rings and fields from scratch, starting with elementary number theory. Different parts are at different levels of completion.
Notes on linear algebra: Attempt at a rigorous introduction to linear algebra. Currently, only the basics of matrix algebra are finished.