Related papers: Applied Categories and Functors for Undergraduates
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
Robust preparation of future secondary mathematics teachers requires attention to the acquisition of mathematical knowledge for teaching. Many future teachers learn mathematics content primarily through mathematics major courses that are…
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…
This textbook is an introduction to economic networks, intended for students and researchers in the fields of economics and applied mathematics. The textbook emphasizes quantitative modeling, with the main underlying tools being graph…
This is an introductory machine-learning course specifically developed with STEM students in mind. Our goal is to provide the interested reader with the basics to employ machine learning in their own projects and to familiarize themself…
We introduce a newly designed undergraduate-level interdisciplinary course in scientific computing that aims to prepare students as the next generation of research-oriented computational scientists and engineers. The course offers students…
These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is…
A series of lecture notes on the elementary theory of algebraic numbers, using only knowledge of a first-semester graduate course in algebra (primarily groups and rings). No prerequisite knowledge of fields is required. Based primarily on…
These notes were originally developed as lecture notes for a category theory course. They should be well-suited to anyone that wants to learn category theory from scratch and has a scientific mind. There is no need to know advanced…
Special functions and their applications in quantum mechanics and electromagnetism: Course notes.
Traditional approaches to undergraduate-level quantum mechanics require extensive mathematical preparation, preventing most students from enrolling in a quantum mechanics course until the third year of a physics major. Here we describe an…
An introduction to applied mathematics written for students in engineering and science. Focus is on a rigorous presentation that also builds understanding by discussion, analogy, and examples. Discussion of concepts involved in modeling…
An annotation consists of a portion of information that is associated with a piece of content in order to explain something about the content or to add more information. The use of annotations as a tool in the educational field has positive…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
These are the notes for a minicourse held in Odessa (2016) and Belo Horizonte (2017). My aim was to provide a short introduction to basic notions of category theory and representation theory of finite-dimensional algebras. We learnt the…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications:…
Graduated locally finitely presentable categories are introduced, examples include categories of sets, vector spaces, posets, presheaves and Boolean algebras. A finitary functor between graduated locally finitely presentable categories is…
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…
This is the text for a one quarter or one semester undergraduate course on quantum computing that has been given at the University of California Santa Cruz. It is intended for students in the physical sciences who have already studied…