Algebra

Last modified: 2026-11-03 15:17:03 (PST)

The algebra notes are split across these pages:

• Equalities, Inequalities and Minimizers: equalities, inequalities, powers, square roots and absolute values, minima and maxima, and global and local minimizers.
• Convexity, Infimum and Sums: convex functions, the infimum and supremum, sums, products and quotients, summation notation, limits of sums, and notational shorthands.
• Polynomials, Exponentials and Logarithms: polynomials, affine and linear functions of one variable, limits of sequences, series, exponentials and logarithms.
• Trigonometry: cosine and sine on the unit circle, and the identities later pages use.
• Complex Numbers: complex numbers and their arithmetic.

A link to a section, theorem or definition on this page from before the split goes on to the page that now holds it.

1 Further reading

• Abramson et al. [1] is a free online textbook on algebra and trigonometry. It covers equations, inequalities, polynomials, exponentials, logarithms, and trigonometry, which overlap with the algebra in these notes.
• Rudin [2] develops the real numbers, including the least upper bound property behind the infimum and supremum.

References

[1]

J. Abramson et al., Algebra and trigonometry, 2nd ed. OpenStax, 2021. Available: https://openstax.org/books/algebra-and-trigonometry-2e/pages/preface

[2]

W. Rudin, Principles of mathematical analysis, 3rd ed. in International series in pure and applied mathematics. New York: McGraw-Hill, 1976.