GaDOE is using a new technical specification by the IMS Global Learning Consortium (IMS Global) called the Competency and Academic Standards Exchange (CASE) to enable a machine readable, linked data versions of state standards. With CASE, open-educational resources can be more easily tagged and discovered. Districts and individual educators can build crosswalks to their local learning targets, organize assessment results, and discover content through these crosswalks. The CASE format enables teaching, learning, and assessment software systems to access or consume competency frameworks and crosswalks.

The information shared within this website was carefully curated and designed to promote quality online teaching and learning experiences for Precalculus faculty and students within the University of North Carolina System.

Mathematical principles and processes specifically for elementary teachers. Includes problem solving, set theory, properties and operations with number systems. This course uses MyOpenMath.

My goal is to merge New York State standards with Common Core Standards and Integrated Algebra Regent Standards for our 8th grade curriculum.

These are full-course openly licensed resources for districts interested in exploring OER options when considering core instructional materials for district adoption.

This resource is a collection of short closed-captioned lectures that accompany the power points covering most of chapters 1,2,3, 6, 9, 11, 12, and 13 of the OpenStax Introductory Statistics book. The Power Points are provided in both .PPT and .PDF format to accommodate downloading ease. The notes are in .DOC format.

This calculus course covers differentiation and integration of functions of one variable, and concludes with a brief discussion of infinite series. Calculus is fundamental to many scientific disciplines including physics, engineering, and economics.
Course Format
This course has been designed for independent study. It includes all of the materials you will need to understand the concepts covered in this subject. The materials in this course include:

Lecture Videos with supporting written notes
Recitation Videos of problem-solving tips
Worked Examples with detailed solutions to sample problems
Problem sets with solutions
Exams with solutions
Interactive Java Applets (“Mathlets”) to reinforce key concepts

Content Development
David Jerison   
Arthur Mattuck   
Haynes Miller   
Benjamin Brubaker   
Jeremy Orloff
Heidi Burgiel   
Christine Breiner   
David Jordan   
Joel Lewis
About OCW Scholar
OCW Scholar courses are designed specifically for OCW’s single largest audience: independent learners. These courses are substantially more complete than typical OCW courses, and include new custom-created content as well as materials repurposed from previously published courses.

IM K–5 Math is a problem-based core curriculum rooted in content and practice standards to foster learning and achievement for all. Students learn by doing math through solving problems, developing conceptual understanding, and discussing and defending their reasoning. Teachers build confidence with lessons and curriculum guides that help them facilitate learning and help students make connections between concepts and procedures.

Every activity and lesson in IM K–5 Math tells a coherent mathematical story across units and grade levels based on both the standards and research-based learning trajectories. This allows students the opportunity to view mathematics as a connected set of ideas and offers them access to mathematics when developed into the overarching design structure of the curriculum.

The first unit in each grade level provides lesson structures which establish a mathematical community and invite students into the mathematics with accessible content. Each lesson offers opportunities for the teacher and students to learn more about one another, develop mathematical language, and become increasingly familiar with the curriculum routines. The use of authentic contexts and adaptations provides students opportunities to bring their own experiences to the lesson activities and see themselves in the materials and mathematics.

This Geometry Concept Collection is a rigorous presentation of high school geometry. It is fully correlated with the Common Core State Standards.

Introduction to econometric models and techniques, simultaneous equations, program evaluation, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable models. May not count toward HASS requirement.

This course serves as an introduction to major topics of modern enumerative and algebraic combinatorics with emphasis on partition identities, young tableaux bijections, spanning trees in graphs, and random generation of combinatorial objects. There is some discussion of various applications and connections to other fields.

18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.

This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy type; inverse scattering transform; and group theory. Examples are taken from fluid and solid mechanics, acoustics, quantum mechanics, and other applications.

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space.
MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.

This course continues the content covered in 18.100 Analysis I. Roughly half of the subject is devoted to the theory of the Lebesgue integral with applications to probability, and the other half to Fourier series and Fourier integrals.

This course begins with an introduction to the theory of computability, then proceeds to a detailed study of its most illustrious result: Kurt Gödel’s theorem that, for any system of true arithmetical statements we might propose as an axiomatic basis for proving truths of arithmetic, there will be some arithmetical statements that we can recognize as true even though they don’t follow from the system of axioms. In my opinion, which is widely shared, this is the most important single result in the entire history of logic, important not only on its own right but for the many applications of the technique by which it’s proved. We’ll discuss some of these applications, among them: Church’s theorem that there is no algorithm for deciding when a formula is valid in the predicate calculus; Tarski’s theorem that the set of true sentence of a language isn’t definable within that language; and Gödel’s second incompleteness theorem, which says that no consistent system of axioms can prove its own consistency.

This course provides an introduction to nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering. The course concentrates on simple models of dynamical systems, mathematical theory underlying their behavior, their relevance to natural phenomena, and methods of data analysis and interpretation. The emphasis is on nonlinear phenomena that may be described by a few variables that evolve with time.