university levels of education Algebra 103 I — V
Algebra 103, Deep Algebra — handmade, no ads, no sign-ups. Every lecture is kept whole and shown whole: nothing is summarised, so what you see is the lecture as it was written. 36,943 words across 25 lectures, from polynomial rings and the Factor Theorem to number theory for algebra. Twenty-one ways through the same text, forty-six palettes on a white default with dark a click away, twelve layouts and colours you can set yourself. The source is native LaTeX, so the mathematics needed no repair at all: every formula is the author's own markup, rendered as written.
- 001
Lectures 1–10
Lectures 1 to 10. Polynomial Review, Long Division, Synthetic Division, Remainder Theorem, and Factor Theorem, Multiple Roots, Complex Roots, Conjugate Root Theorem, and Root Multiplicity, Rational Root Theorem, Descartes' Rule of Signs, Upper & Lower Bound Theorems, Partial Fractions, Polynomial Identities, Completing the Square, and Advanced Rational Expressions, Function Transformations and 5 more, ending on Rational Functions: Domains, Asymptotes, Holes, Intercepts, and Graphing. 8,561 words across 10 lectures.
live - 002
Lectures 11–20
Lectures 11 to 20. Rational Equations and Rational Inequalities, Complex Numbers: The Imaginary Unit, Arithmetic, Conjugates, Polar Representation, and Applications, Systems of Linear Equations: Gaussian Elimination, Row Operations, and Augmented Matrices, Matrices: Matrix Operations, Matrix Multiplication, Identity Matrices, Inverses, and Applications, Determinants: Minors, Cofactors, Expansion, Properties, Cramer’s Rule, and Geometric Meaning and 5 more, ending on Nonlinear Systems of Equations: Graphical Interpretation, Algebraic Methods, Tangency, and Applications. 15,701 words across 10 lectures.
live - 003
Lectures 21–25
Lectures 21 to 25. Advanced Sequences and Series: Recursive Models, Partial Sums, Infinite Geometric Series, Convergence, and Applications, Mathematical Induction and Recurrence Relations, The Binomial Theorem and Combinatorial Algebra, Advanced Polynomial Root Theory and Algebraic Modeling, Optimization, and Comprehensive Problem Solving. 12,681 words across 5 lectures.
live - 004
The whole course
All 25 lectures, opened without a filter. 36,943 words, 18,191 blocks, 13 tables and 0 paired examples, with a glossary of 74 entries and a search index of 2,018 words. Twenty-one ways through the same text. Six read it — one lecture entire, an index of every lecture number down the left, a reader that hands you a single section at a time, a continuous scroll, an outline of the section headings, and a syllabus of the whole course. Eight take it apart — every Spanish line beside its English, the glossary lifted out of the tables, the tables on their own, flashcards Spanish side first, the practice questions, a drill that pulls a random example in either direction, and the objectives and closing summaries. Seven keep track — homework, cultural notes, an accent-insensitive search across every block, starred lines, a page of your own notes per lecture, a progress board, and a printable handout. Forty-six colour palettes on a white default with dark one click away, eight colour roles editable by hand, twelve page layouts from a narrow reading column through ruled notebook paper and two magazine columns to a monospaced terminal, seven typefaces with a separate face for the Spanish, and sliders for text size, leading and line length. The English can be hidden to read the Spanish cold, or the Spanish hidden to work back the other way. Progress, stars and notes autosave, with JSON export and import.
live