Active Calculus: Single Variable
Matthew Boelkins; David Austin; Christina Safranski; Steven Schlicker
Mathematics
91 selected books, grouped by course
Study guides
Compare three books with short trial tasks, follow a six-step reading route, and test your reasoning with worked examples and changed assumptions.
MathematicsAbstract Algebra
Abstract algebra: name the operation a map must preserve
Compare three algebra routes and solve original quotient-map cases, distinguishing additive structure, multiplication and the limits of an isomorphism claim.
MathematicsCalculus and Multivariable CalculusChoose a calculus text and connect rates to accumulation
Compare two free calculus texts with Thomas, follow six concrete study tasks, and audit a worked rate-and-accumulation problem.
MathematicsComplex AnalysisComplex analysis: a contour is part of the hypothesis
Compare analytic and geometric texts, compute a double-pole residue, then change the contour and explain exactly why the original Cauchy-formula argument fails.
MathematicsDifferential EquationsDifferential equations: solve, match and check the model
Compare three ODE routes and solve original switching-input problems, distinguishing a discontinuous forcing term from a separately imposed jump in the state.
MathematicsDiscrete MathematicsDiscrete structures: count only assignments that can coexist
Compare three discrete mathematics texts and solve original matching problems using exact counting, Hall obstructions and a minimal repair.
MathematicsLinear AlgebraLinear algebra: choose a route from equations to subspaces
Compare three linear algebra routes, test each book with a short task, and solve original rank, nullspace and least-squares problems with explicit checks.
MathematicsProbability and StatisticsProbability foundations: count the experiment you actually observed
Compare probability and statistics reading routes, then solve sampling and reveal-protocol problems that separate counting, conditioning and independence.
MathematicsReal AnalysisReal analysis: make the quantifiers do the work
Compare three analysis texts, build epsilon proofs and test uniform convergence with original examples whose peaks move as the index grows.
A place to start
Mathematics: move from calculation to proof at the right pace
Suggested reading compiled by this site for university students and independent learners. This is not an official university reading plan. Check your own syllabus before buying; editions and exercise numbers differ.
Browse all books ↓Choose for your course
Choose by course level, not by the most advanced title. Calculus and linear algebra build computational tools; proof-based courses such as real analysis or abstract algebra require a different way of reading. Check prerequisites before treating a rigorous text as a first introduction.
Suggested reading approach
- For a new definition, write one example and one non-example. Attempt exercises before consulting worked solutions; checking each algebraic step matters as much as the final answer.
- When the course turns proof-based, restate the claim in your own words, identify what is assumed, and test the proof on small cases before reading ahead.
Browse by course
Books are grouped by the course they are usually read for, then ordered from introductory to advanced.
Choose a course
Calculus and Multivariable Calculus 6 books
Study guides: Choose a calculus text and connect rates to accumulation →
Linear Algebra 6 books
Study guides: Linear algebra: choose a route from equations to subspaces →
Real Analysis 7 books
Study guides: Real analysis: make the quantifiers do the work →
Abstract Algebra 7 books
Study guides: Abstract algebra: name the operation a map must preserve →
Probability and Statistics 8 books
Study guides: Probability foundations: count the experiment you actually observed →
Differential Equations 5 books
Study guides: Differential equations: solve, match and check the model →
Discrete Mathematics 7 books
Study guides: Discrete structures: count only assignments that can coexist →
Topology and Geometry 6 books
Complex Analysis 7 books
Study guides: Complex analysis: a contour is part of the hypothesis →
