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university levels of education Algebra I — V

Five levels in one reader, from the first negative number to De Moivre’s theorem, matrices and the binomial theorem — handmade, no ads, no sign-ups. A hundred and forty written lectures with the mathematics properly typeset, four hundred and thirty-six worked examples solved step by step with the reasoning shown, five hundred and sixty practice questions with hints and answers, quizzes, and over five hundred unsolved problems to do on your own, in nineteen ways of studying including a continuous read of a whole course. Start at whichever level you need; the last entry opens all five courses as one book.

§ levels 6 live
  1. 001

    Algebra I

    Foundations and Expressions. Arithmetic put on a firm footing before any letters appear — signed integers, order of operations, absolute value, fractions, decimals and percents, ratio and proportion, the three exponent rules, scientific notation, roots, and greatest common factor against lowest common multiple. Then the language of algebra itself: terms and like terms, the distributive law, evaluating an expression at a value, translating a sentence into symbols, and simplifying what you end up with. Twenty-one lectures, 254 questions. Every lecture carries a written explanation with the mathematics properly typeset, a table of the formulas that matter, defined terms and the mistakes to watch for, worked examples revealed step by step with the reasoning beside each step, practice questions with hints, a quiz, and unsolved problems to do on your own — studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.

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  2. 002

    Algebra II

    Equations, Inequalities and Graphs. Solving for the unknown and reading the answer off a grid — one-step, two-step and multi-step equations, variables on both sides, equations with fractions, literal equations rearranged for a named letter, and the cases that give no solution or every solution. Then inequalities and their compound and absolute-value forms, the coordinate plane, slope, all three forms of a line, parallels and perpendiculars, distance and midpoint, and systems solved by graphing, substitution and elimination. Thirty-one lectures, 377 questions. Every lecture carries a written explanation with the mathematics properly typeset, a table of the formulas that matter, defined terms and the mistakes to watch for, worked examples revealed step by step with the reasoning beside each step, practice questions with hints, a quiz, and unsolved problems to do on your own — studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.

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  3. 003

    Algebra III

    Polynomials, Factoring and Quadratics. Expressions with more than one term, taken apart and put back together — adding, multiplying and dividing polynomials, the special products, and long and synthetic division. Then every route into a factorisation: common factors, grouping, trinomials with and without a leading coefficient, differences of squares, sums and differences of cubes. Quadratics solved four ways, the discriminant, vertex and axis of symmetry, and the parabola itself. Closing with radicals, rationalised denominators, and rational expressions simplified, combined and solved. Thirty-nine lectures, 472 questions. Every lecture carries a written explanation with the mathematics properly typeset, a table of the formulas that matter, defined terms and the mistakes to watch for, worked examples revealed step by step with the reasoning beside each step, practice questions with hints, a quiz, and unsolved problems to do on your own — studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.

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  4. 004

    Algebra IV

    Functions, Logarithms and Advanced Topics. Where school algebra hands over to the first year of a degree — function notation, domain and range, composition and inverses, transformations and piecewise definitions. Exponential growth and decay, logarithms and their laws, and the equations that need them. Arithmetic and geometric sequences, series and sigma notation. A chapter of word problems worth the name, and then complex numbers, matrix arithmetic, determinants and Cramer's rule, the binomial theorem, the remainder and factor theorems, the rational root theorem, and the end behaviour of a polynomial. Twenty-nine lectures, 372 questions. Every lecture carries a written explanation with the mathematics properly typeset, a table of the formulas that matter, defined terms and the mistakes to watch for, worked examples revealed step by step with the reasoning beside each step, practice questions with hints, a quiz, and unsolved problems to do on your own — studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.

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  5. 005

    Algebra V

    Complex Numbers, Polynomials, Matrices and Counting. The capstone course. The imaginary unit and the complex plane, arithmetic and division by conjugates, polar form, De Moivre's theorem and the roots of unity. The full theory of polynomial equations — long and synthetic division, the remainder and factor theorems, the rational root theorem, the fundamental theorem of algebra with multiplicity, and Vieta's formulas. Matrices with determinants, inverses, Cramer's rule and the plane transformations they perform. And the art of counting: factorials, permutations and combinations, the binomial theorem, Pascal's triangle and classical probability. Twenty lectures, 259 questions. Every lecture carries a written explanation with the mathematics properly typeset, a table of the formulas that matter, defined terms and the mistakes to watch for, worked examples revealed step by step with the reasoning beside each step, practice questions with hints, a quiz, and unsolved problems to do on your own — studied through nineteen modes, from flashcards and drills to timed exams and a continuous read of the whole course as one page.

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  6. 006

    The whole of algebra

    Every level at once — all five courses, twenty chapters, 140 lectures and more than 1,700 questions read as one book. The whole-course view strings every lecture into a single continuous page from integer addition to the binomial theorem, the formula sheet and glossary pool the entire subject, and mixed exams draw questions from all five courses at once. This is the one to open when you want to read algebra from the beginning or revise across course boundaries rather than work through a single level.

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