mathematics

Adding and Subtracting Fractions with Common Denominators

Handbook guide to adding and subtracting fractions with common denominators, with rules, worked examples, verification, common errors and practical.

Addition, Subtraction and Multiplication of Polynomials

Handbook guide to addition, subtraction and multiplication of polynomials, with formulas, methods, worked examples, checks and engineering-oriented applica.

Advanced Algebra Notation and Reading Conventions

Handbook guide to advanced algebra notation and reading conventions, covering definitions, key results, methods, verification checks and worked examples.

Affine Varieties

Handbook guide to Affine Varieties, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Engineering Mathematics14 Aug 2026 · 6 min read

Affine Varieties and Finite Generation

Handbook guide to affine varieties and finite generation with core definitions, structural results, reasoning methods and verification checks.

Engineering Mathematics14 Aug 2026 · 10 min read

Affine Varieties and Polynomial Zero Sets

Handbook guide to affine varieties and polynomial zero sets, covering definitions, key results, methods, verification checks and worked examples.

Algebra of Functions and Difference Quotients

Handbook guide to algebra of functions and difference quotients, with formulas, methods, worked examples, checks and engineering-oriented applications.

Algebraic Closures

Handbook guide to Algebraic Closures, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Analysing Graphs of Quadratic Functions

Handbook guide to analysing graphs of quadratic functions, with formulas, methods, worked examples, checks and engineering-oriented applications.

Applications of Right Triangles

Handbook guide to applications of right triangles, with formulas, methods, worked examples, checks and engineering-oriented applications.

Applications of Sylow Theory

Handbook guide to Applications of Sylow Theory, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Arithmetic in Dedekind Domains

Handbook guide to Arithmetic in Dedekind Domains, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Arithmetic Sequences and Series

Handbook guide to arithmetic sequences and series, with formulas, methods, worked examples, checks and engineering-oriented applications.

Base Change in Tensor Products

Handbook guide to Base Change in Tensor Products, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Basic Geometry for Algebra and Trigonometry

Handbook guide to basic geometry for algebra and trigonometry, with formulas, methods, worked examples, checks and engineering-oriented applications.

Basics of Equation Solving

Handbook guide to basics of equation solving, with formulas, methods, worked examples, checks and engineering-oriented applications.

Bilinear Forms and Orthogonality

Handbook guide to bilinear forms and orthogonality, covering definitions, key results, methods, verification checks and worked examples.

Cancelling Factors in Algebraic Fractions

Handbook guide to cancelling factors in algebraic fractions, with rules, worked examples, verification, common errors and practical engineering applications.

Engineering Mathematics14 Aug 2026 · 10 min read

Categories, Products, Coproducts and Functors

Handbook guide to categories, products, coproducts and functors with core definitions, structural results, reasoning methods and verification checks.

Categories, Universal Constructions and Diagrams

Handbook guide to categories, universal constructions and diagrams, covering definitions, key results, methods, verification checks and worked examples.

Chain Complexes

Handbook guide to Chain Complexes, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Chain Complexes, Chain Maps and the Snake Lemma

Handbook guide to chain complexes, chain maps and the snake lemma with core definitions, structural results, reasoning methods and verification checks.

Chain Conditions and the Generator Lemma

Handbook guide to Chain Conditions and the Generator Lemma, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Choice Principles and Maximality Methods

Handbook guide to choice principles and maximality methods, covering definitions, key results, methods, verification checks and worked examples.

Circular Functions: Graphs and Properties

Handbook guide to circular functions: graphs and properties, with formulas, methods, worked examples, checks and engineering-oriented applications.

Cofunction, Double-Angle and Half-Angle Identities

Handbook guide to cofunction, double-angle and half-angle identities, with formulas, methods, worked examples, checks and engineering-oriented applications.

Combinatorics: Combinations

Handbook guide to combinatorics: combinations, with formulas, methods, worked examples, checks and engineering-oriented applications.

Combinatorics: Permutations

Handbook guide to combinatorics: permutations, with formulas, methods, worked examples, checks and engineering-oriented applications.

Commutative Rings, Domains, Units and Subrings

Handbook guide to commutative rings, domains, units and subrings, covering definitions, key results, methods, verification checks and worked examples.

Engineering Mathematics14 Aug 2026 · 14 min read

Comparison and One-Variable Relationship Models

Handbook guide to comparison and one-variable relationship models, with rules, worked examples, verification, common errors and practical engineering.

Complex Numbers

Handbook guide to complex numbers, with formulas, methods, worked examples, checks and engineering-oriented applications.

Complex Numbers in Trigonometric Form

Handbook guide to complex numbers in trigonometric form, with formulas, methods, worked examples, checks and engineering-oriented applications.

Complex Numbers, Roots of Unity and Cyclotomic Polynomials

Handbook guide to complex numbers, roots of unity, with definitions, key results, methods, verification checks and worked examples.

Composition Series

Handbook guide to Composition Series, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.

Engineering Mathematics14 Aug 2026 · 9 min read

Composition Series, Solvable Groups and Nilpotent Groups

Composition Series, Solvable Groups and Nilpotent Groups: core definitions, structural results and verification methods in abstract algebra.

Engineering Mathematics14 Aug 2026 · 6 min read

Computing Ext, Tor and Base Change

Handbook guide to computing ext, tor and base change with core definitions, structural results, reasoning methods and verification checks.

Computing Galois Groups and Finite Fields

Handbook guide to computing galois groups and finite fields with core definitions, structural results, reasoning methods and verification checks.

Computing Galois Groups Directly

Handbook guide to Computing Galois Groups Directly, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Engineering Mathematics14 Aug 2026 · 14 min read

Consecutive Integer and Number-Relationship Problems

Handbook guide to consecutive integer and number-relationship problems, with rules, worked examples, verification, common errors and practical engineering.

Cosets, Normal Subgroups and Homomorphisms

Handbook guide to Cosets, Normal Subgroups and Homomorphisms, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Engineering Mathematics14 Aug 2026 · 9 min read

Cosets, Normal Subgroups, Quotient Groups and Homomorphisms

Cosets, Normal Subgroups, Quotient Groups and Homomorphisms: core definitions, structural results and verification methods in abstract algebra.

Engineering Mathematics14 Aug 2026 · 12 min read

Cosets, Subgroup Index and Finite-Group Divisibility

Handbook guide to cosets, subgroup index and finite-group divisibility, covering definitions, key results, methods, verification checks and worked examples.

Crossed Product Algebras and Spectral Sequences

Handbook guide to crossed product algebras and spectral sequences, covering definitions, key results, methods, verification checks and worked examples.

Cyclic and Kummer Extensions

Handbook guide to Cyclic and Kummer Extensions, with key definitions, results, formulas, reasoning methods and worked examples for abstract algebra.

Cyclic Extensions, Kummer Extensions and Solvability by Radicals

Cyclic Extensions, Kummer Extensions and Solvability by Radicals: core definitions, structural results and verification methods in abstract algebra.

Cyclotomic Fields

Handbook guide to Cyclotomic Fields, covering core definitions, key results, formulas, reasoning methods and worked examples in graduate abstract algebra.