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List of open textbooks which meet the evaluation criteria of the AIM editorial board as being suitable for use in university courses. Books grouped by topic with description and list of features. Various licenses.
Introductory textbook allowing students to learn how to apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories in preparation for advanced mathematical courses. CC BY-NC-ND (Creative Commons Attribution-NonCommercial-NoDerivatives) license.
Textbooks designed for first or second year undergraduate course for maths majors, especially those who will go on to teach. Topics covered include: set theory, counting techniques, sequences, and graph theory. CC BY-SA (Creative Commons Attribution-ShareAlike) license.
Motivated by questions in cosmology this book uses Möbius transformations to develop hyperbolic, elliptic, and Euclidean geometries - three possibilities for the global geometry of the universe. Written for students who have taken vector calculus. Includes companion guide with online computational tools. CC BY-SA (Creative Commons Attribution-ShareAlike) license.
Textbook covering the basic concepts of statistics. Topics covered include: descriptive statistics, numerical descriptions, bi-variate statistics, linear regression, probability theory, and research methods. CC BY-SA (Creative Commons Attribution-ShareAlike) license.
Textbook designed for one-semester course in mutivariable calculus. Topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. CC BY (Creative Commons Attribution) license.
Collection of textbooks published by OpenStax designed for maths courses ranging from preparatory to advanced levels. Books available on algebra, trigonometry, calculus and statistics. Includes instructor and student resources. CC BY (Creative Commons Attribution) license.
Online platform with interactive mathematics and statistics exercises that enables higher education teachers to find and create openly licensed resources. Winner of a 2019 Open Education Award. Content continuing to be released by current publicly available resources are CC BY-NC-SA (Creative Commons Attribution-NonCommercial-ShareAlike) licensed.
Collection of support materials for students and lecturers looking for post-16 mathematics help. Developed by a group of UK universities and organisations to allow students to study important areas of pre-university mathematics which may be new to them and which is required for their course. CC BY-NC-ND (Creative Commons Attribution-NonCommerical-NoDerivatives) license.
Podcast series from Oxford Mathematics exploring the power and beauty of their subject. Only episodes with a (CC) symbol next to their title are available under a CC BY-NC-SA (Creative Commons Attribution-NonCommercial-ShareAlike) license.
Collection of interdisciplinary videos investigating biological systems using a physical sciences perspectives. Topics cover include algebra, calculus, probability and statistics, spatiality, and their biological applications. CC BY-SA (Creative Commons Attribution-ShareAlike) license.
Courses in mathematics as taught at the Massachusetts Institute of Technology. Content varies but can include lecture notes, videos, assignments with solutions etc. CC BY-NC-SA (Creative Commons Attribution-NonCommercial-ShareAlike) license but courses may refer to copyright material.
Mathematics and statistics courses ranging from introductory to advanced level from the Open University. Courses cover a wide range of topics including:number theory, geometry, bayesian stastics, and surfaces. CC BY-NC-SA (Creative Commons Attribution-NonCommercial-ShareAlike) license.
Online self-directed courses exploring the real-world applications of mathematics through algebra, calculus, statistics, and geometry. Asides from final exams content created by Saylor Academy is CC BY (Creative Commons Attribution) licensed. Various licenses for third party material.
Courses taught in the Masters of Applied Mathematics at the Delft University of Technology. Content varies but can include recorded lectures, readings, exams and exercises. CC BY-NC-SA (Creative Commons Attribution-NonCommercial-ShareAlike) license.