📋 Changes in this PR: Equalities, Inequalities and Minimizers, Complex Numbers, Polynomials, Exponentials and Logarithms, Convexity, Infimum and Sums, Trigonometry, Algebra, Derivatives and Taylor Series, Double Integrals and Fubini’s Theorem, Integrals and the Fundamental Theorem of Calculus, Calculus, Dependency Tree, Expressions and Algorithms, Functions, Growth Rates, Math for Data Science, Indicator Functions, Induction and Recursion, Complex Vectors and Matrices, Diagonalization and Cholesky, Direct Sums and Orthogonal Complements, Inner Products and Orthogonality, Matrices, Projections and Linear Systems, Column Space, Null Space and Rank-Nullity, Special Matrices and Decompositions, Subspaces and Rank, Vectors, Linear Algebra, Additivity, Measurable Functions and Integrals, \(L^p\) Spaces, Measures and Probability Measures, Product Measures, Sigma-Algebras, Measures, Notation, Number Systems, Quadratic Minimization under Linear Constraints, Convexity in Several Variables, Critical Points and Optimality Conditions, Gradient Descent, Newton’s Method, Quasi-Newton Methods, Optimization, Proof Writing, Relations, Sets and Functions, Sets, Vector Calculus
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Algebra

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.