Library

OpenStax

The arithmetic foundation for algebra: whole numbers, integers, fractions, decimals, percents, and a first look at equations, graphs, and geometry. Working these exercises builds the number fluency and step-by-step habits that a first algebra course assumes.

OpenStax

A first algebra course: linear equations and inequalities, graphing, systems, polynomials and factoring, rational expressions, radicals, and quadratic equations. The exercises train the core skill everything later builds on — translating a problem into an equation and solving it methodically.

OpenStax

Second-course algebra centered on functions: quadratic, rational, radical, exponential, and logarithmic functions, plus conics and sequences. Solving these problems develops the symbolic fluency and graph sense that college algebra and precalculus take for granted.

OpenStax

A complete precalculus toolkit: equations and inequalities, polynomial, rational, exponential, and logarithmic functions, trigonometry, systems, analytic geometry, and a first look at limits. These exercises build the function fluency and algebraic stamina calculus demands.

OpenStax

A liberal-arts tour of mathematics in use: logic, sets, number systems, personal finance, probability, statistics, geometry, voting and apportionment, and graph theory. The exercises practice quantitative reasoning on everyday questions of money, fairness, risk, and data.

Portland Community College

Mathematics for informed citizenship: logical reasoning and problem solving, financial math, statistics, probability, and the mathematics of democracy — voting and apportionment. The exercises practice applying math where daily life actually demands it: loans, risk, data, and elections.

Matthew Boelkins

Single-variable calculus built around guided activities: understanding and computing derivatives, their applications, definite integrals, differential equations, and Taylor series. The activity-style problems have you construct each idea before using it — understanding first, procedure second.

Long, Keller & Schlicker

Multivariable calculus in the same activity-driven style as Active Calculus: vectors and vector-valued functions, functions of several variables, partial derivatives and optimization, multiple integrals, and the vector calculus of line and surface integrals through Green's, Stokes' and the Divergence theorems.

Steve Simonds & Alex Jordan

Differential calculus drilled lab-style: rates of change, limits and continuity, the derivative and antiderivatives, derivative formulas, the chain rule, implicit differentiation, and curve analysis. Short, focused exercises test each concept right after it appears — ideal alongside any first calculus course.

Jiří Lebl

A first course in differential equations for science and engineering: first- and second-order ODEs, systems, Fourier series and PDEs, the Laplace transform, power-series methods, and nonlinear systems. The problems build both solution technique and a modeling instinct for when each tool applies.

Thomas W. Judson

Differential equations with a systems-first flavor: first-order equations, linear systems and the phase plane, second-order equations, and the Laplace transform. The problems practice both solving equations exactly and reading long-run behavior straight from a system’s structure.

David Austin

Linear algebra developed visually and computationally: linear systems, matrices and linear combinations, invertibility and bases, eigenvalues, orthogonality and least squares, and the singular value decomposition. The exercises connect geometric intuition to matrix computation and to applications in dynamics and data.

Jim Hefferon

A proof-based first course in linear algebra: linear systems and Gauss’s Method, vector spaces, maps between spaces, determinants, and similarity and eigenvalues. The exercises range from computation to proof, with fully worked answers that model how to write mathematics well.

Peter Selinger

A full first course in linear algebra grown from the Kuttler/Lyryx text: systems of equations, vectors, matrices, determinants, eigenvalues, abstract vector spaces, linear transformations, and inner product spaces, with applications from resistor networks to principal component analysis. Most exercises come with the book's own answers.

Stephen Davies

Discrete math for computer science in quick question-and-answer strides: sets and partitions, relations and functions, probability, counting, binary and hexadecimal numbers, and propositional and predicate logic. Each drill poses a short question and immediately checks the answer, building fluency step by step.

Oscar Levin

A first course in discrete mathematics: counting, sequences, symbolic logic and proof, and graph theory, plus a closing pair of sections on generating functions and number theory. Investigate-first problems — knights and knaves, rook paths, Rubik's cube distributions — motivate each technique before it is formalized.

John Hammond

A bridge into discrete mathematics: sets and symbols, symbolic logic and proof techniques, classic number theory, sequences, recurrence and induction, and counting. The exercises train the transition skill this course exists for — turning an intuition into a precise, correct proof.

Mitchel T. Keller & William T. Trotter

Combinatorics for mathematics and computer science: counting with strings, sets, and binomial coefficients, induction, graph theory, partially ordered sets, inclusion–exclusion, and generating functions. The exercises build the discrete problem-solving repertoire behind algorithms and probability.

Kan Onn Kit

A full first course in abstract algebra: groups, subgroups, homomorphisms and quotients through the Sylow theorems, then rings, ideals and factorization, and fields through Galois theory and the fundamental theorem of algebra. Every proof step is spelled out rather than left as an exercise for the reader.

OpenStax

The classic college introduction to statistics: sampling, descriptive statistics, probability, distributions, the Central Limit Theorem, confidence intervals, hypothesis testing, chi-square, regression, and ANOVA. The exercises practice the full path from raw data to a defensible statistical conclusion.

OpenStax

Statistics for a first (AP-aligned) course: describing data, probability, random variables, the normal distribution, confidence intervals, hypothesis tests, and regression. The exercises build statistical judgment — choosing the right procedure, running it, and saying what the result actually means.

Diez, Barr & Çetinkaya-Rundel

An algebra-based statistics course built around real datasets: study design and sampling, data summaries, probability and distributions, and statistical inference for both categorical and numerical data, closing with simple and multiple regression.

OpenStax

Introductory statistics with a business lens: descriptive statistics, probability, distributions, confidence intervals, hypothesis tests, ANOVA, and regression, applied to finance, marketing, and operations data. The exercises practice turning business data into decisions you can defend.

Paul E. Pfeiffer

A rigorous first course in applied probability: probability systems and conditional probability, random variables and distributions, mathematical expectation, variance and covariance, and conditional expectation. Every problem set ships fully worked solutions, many alongside computational transcripts.

OpenStax

Algebra-based physics from mechanics through modern physics: motion, forces, energy, fluids, heat, waves and sound, electricity and magnetism, optics, and atomic and nuclear physics. The problems train the core physics move — model the situation, pick the principle, and carry units through to a checked answer.

OpenStax

Calculus-based mechanics: kinematics, Newton’s laws, work and energy, momentum, rotation, equilibrium, gravitation, fluids, oscillations, waves, and sound. These problems develop the ability to set up a physical model with calculus and drive it to a quantitative answer.

OpenStax

Calculus-based thermodynamics and electromagnetism: heat and kinetic theory, the laws of thermodynamics, electric fields and Gauss’s law, potential, circuits, magnetism, induction, and electromagnetic waves. The problems build fluency with fields, flux, and circuit reasoning.

OpenStax

Calculus-based optics and modern physics: geometric optics, interference and diffraction, relativity, photons and matter waves, quantum mechanics, and atomic, condensed-matter, nuclear, and particle physics. The problems practice quantitative reasoning where classical intuition stops working.

OpenStax

Two semesters of general chemistry: atomic structure, stoichiometry, bonding, gases, thermochemistry, solutions, kinetics, equilibrium, acid–base chemistry, thermodynamics, electrochemistry, and nuclear chemistry. The exercises drill the quantitative core of chemistry — moles, reactions, and equilibrium reasoning.

Magnus, Button, Trueman & Zach

An introduction to formal logic: symbolizing English in truth-functional and first-order logic, truth tables, interpretations, identity and definite descriptions, with excursions into modal logic and metatheory. Practice problems come with the book's own model answers.