This is a non-exhaustive list of open access curriculua for inquiry based courses in college math. The curricula are sorted by topic. If you have an open access curriculum to add to this list, please email me: frederick.peck@umontana.edu
Discovering the art of mathematics library: The DAoM library includes 11 inquiry-based books freely available for classroom use. These texts can be used as semester-long content for themed courses (e.g. geometry, music and dance, the infinite, games and puzzles), or individual chapters can be used as modules
Intermediate Algebra: A Functional Approach: This social-minded text opens with climate change, ends with climate change, and addresses issues of public health and income inequality in between. The sequence of problems generates intellectual need for students to develop important algebraic tools around functions and mathematical modeling. (Developed by Brendan Kelly and colleagues at Harvard.)
Functions and their Rates of Change: This rich mathematical story blends together elements of precalculus and calculus. This text has a sequence of problems that makes immediate progress on the essential question in calculus— how do we measure change? (Developed by Brendan Kelly and colleagues at Harvard.)
Active Prelude to Calculus: A college-level preparatory text for students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Encourages and promotes an active learning approach, with embedded actvities including interactive Desmos activities and interactive applets. (Part of the Active Calculus sequence, developed by Matt Boelkins and colleagues at Grand Valley State).
Precalculus: This course is designed to prepare students to begin a college level calculus series. Topics in this course include all aspects of trigonometry as well as conic sections, exponential functions, polynomial functions, rational functions and linear functions with an emphasis on rate of change. Strong emphasis is placed on strengthening understanding of algebraic concepts necessary to be successful in a college level calculus series. (Peer reviewed and published in the Journal of IBL in Mathematics)
Trigonometry: Topics addressed in this course include the unit circle, definitions and properties of the six trigonometric functions and their inverses, graphs of these functions, identities associated with these functions, the law of sines, the law of cosines, and applications. (Peer reviewed and published in the Journal of IBL in Mathematics)
Active Learning Materials for Precalculus: Activities for specific topics in Precalculus. (Developed by the Boulder/Omaha Active learning aliance.)
Active calculus: Traditional Calculus sequence (I, II, and III), designed for a more active learning experience for students. Every section of each text has engaging activities for students to complete before and during class, as well as exercises that challenge students to connect and assimilate core concepts. The HTML version of each text offers anonymous interactive WeBWorK exercises, select interactive graphics, and full-color static graphics. (Developed by Matt Boelkins and colleagues at Grand Valley State).
Calculus: Newton, Leibniz, and Robinson meet technology: A "ground-up" redesign of Calculus I and II, focused on developing understanding of rates of change and accumulation. Pat Thompson has spent decades studying student understanding of rates and accumulations. (Research-based with peer-reviewed publications. Developed by Pat Thompson and colleagues at Arizona State University. The curriculum was reviewed for the MAA by David Bressoud).
Functions and their Rates of Change: This rich mathematical story blends together elements of precalculus and calculus. This text has a sequence of problems that makes immediate progress on the essential question in calculus— how do we measure change? (Written by Brendan Kelly and colleagues at Harvard.)
Ideas of Calculus: A very interesting approach to calculus, it doesn't really "cover" the topics in a traditional sequence, but rather instroduces several interesting ideas and concepts related to calculus. (Part of the Discovering the Art of Mathematics library)
See also: Multiple peer reviewed Calculus courses (I, II, and III) are published in the Journal of IBL in Mathematics. Sort by subject and look for "calculus"
Coherent Labs to Enhance Accessible and Rigorous Calculus Instruction (CLEAR Calculus): Project CLEAR Calculus is a research-based effort to make calculus conceptually accessible to more students while simultaneously increasing the coherence, rigor, and applicability of the content learned in the courses. There are 36 labs that can be used as inquiry activities in Calculus I and II. (Research-based with peer reviewed publications. Developed by Michael Oehrtman and colleagues at Oklahoma State University)
To access the instructor materials, use: Username: fpeck Password: 1g7TaRdA
Active Learning Materials for Calculus: Activities for specific topics in Calculus I, II, and III. (Produced by the Boulder/Omaha Active learning aliance.)
Statistical Reasoning—A Modeling and Simulation Approach: A simulation and modeling based approach to probablity and statistics. (Research-based with peer-reviewed publications. initially developed by Andrew Zieffler and colleagues at the University of Minnesota, with extensive modification by Fred Peck at the University of Montana)
An Introduction to Probability and Statistics: Self contained inquiry based treatment of elementary probability and statistics. This includes a basic introduction to data analysis, descriptive statistics, correlation, Venn diagrams, probability, Bayes' Rule, random variables, probability distributions, confidence intervals, and statistical inference. (Peer reviewed and published in the Journal of IBL in Mathematics)
Inquiry Oriented Linear Algebra (IOLA): The Inquiry-Oriented Linear Algebra (IOLA) project focuses on developing student materials composed of challenging and coherent task sequences that facilitate an inquiry-oriented approach to the teaching and learning of linear algebra. The project has also developed instructional support materials to help instructors implement the IOLA tasks in their classrooms. (Research-based, with peer-reviewed publications. Developed by researchers at multiple universities).
To access the materials, use: Username: M602 Password: gogriz
See also: Multiple peer reviewed Linear Algebra courses (undergraduate and graduate) are published in the Journal of IBL in Mathematics. Sort by subject and look for "linear algebra"
Inquiry-Oriented Differential Equations (IODE): A first course in differential equations focused on understanding of the big ideas in first order, second order, nonlinear, and systems of differential equations. The course is designed as a full semester course and topics covered include solving ODEs; numerical, analytic and graphical solution methods; solutions and spaces of solutions; linear systems; linearization; qualitative analysis of both ODEs and linear systems of ODEs; structures of solution spaces. (Research-based with peer reviewed publications. Developed by Chris Rasmussen at San Diego State University, and collaborators from multiple universitites.)
To access the instructor materials, use Password: IODE4me
An Introduction to Proof via Inquiry Based Learning: An IBL task sequence for an introduction to proof course. (Written by Dana Ernst at Northern Arizona)
See also: Multiple peer reviewed Introduction to Proof courses are published in the Journal of IBL in Mathematics. Sort by subject and you will find the Intro to Proof courses under "foundations"
Discovering the Art of Mathematics—Number Theory: Students investigate the intricate patterns and relationships that challenge our understanding of the system of whole numbers. (Part of the Discovering the Art of Mathematics library)
A "do-it-yourself" introduction to number theory: Largely an algebraic study of the standard number–theoretic functions, congruences, primes, quadratic residues, etc., taught by a modified Moore-method involving student presentations and interactions. The notes are intended for a semester-length junior level course for mathematics majors as an introduction both to number theory and to the basic ideas of abstract algebra. (Peer reviewed and published in the Journal of IBL in Mathematics)
Combinatorics through guided inquiry: This book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially, but not exclusively, on the part of combinatorics that mathematicians refer to as "counting." The book consists almost entirely of problems. (Written by Ken Bogart at Hanvover College)
Graphs and Optimization: A freshman level general education course in the elementary theory of graphs and practical graph theoretic optimization problems: Euler paths and Euler circuits, the Traveling Salesman Problem, spanning trees, scheduling problems and planar graphs. (Peer reviewed and published in the Journal of IBL in Mathematics)
Multiple peer reviewed Analysis courses (undergraduate and greaduate, real and complex) are published in the Journal of IBL in Mathematics. Sort by subject and look for "analysis (real)" and "analysis (complex)"
Inquiry Oriented Group Theory: A complete introdutory course in group theory. Includes four core instructional sequences that guide students to reinvent groups, subgroups, isomorphism, and quotient groups. (Research Based with peer-reviewed publications. Developed by Sean Larsen and colleagues at Portland State University).
To access the materials, use: Username: guest Password: guest
The website is under construction, so some support sections are incomplete. The complete curriculum is available under "Units" after you log in.
The peer-reviewed publications that form the research basis for the curriculum are not listed on the website right now. You can find many of them here.
An Inquiry-Based Approach to Abstract Algebra: An IBL task sequence for an undergraduate abstract algebra course that emphasizes visualization. (Written by Dana Ernst at Northern Arizona)
See also: Multiple peer reviewed Abstract Algebra courses (undergraduate) are published in the Journal of IBL in Mathematics. Sort by subject and look for "group theory"
Multiple peer reviewed Geometry (Euclidian and non-Euclidian) courses are published in the Journal of IBL in Mathematics. Sort by subject and look for "geometry"
Multiple peer reviewed Topology courses are published in the Journal of IBL in Mathematics. Sort by subject and look for "topology"
For more curricula, visit the Journal for Inquiry-Based Learning in Mathematics (open access)
For activities and pedagogical ideas, see the journal PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies (not open access)