# OPEN CONTENT

## LINEAR ALGEBRA II

This course completes first to second year Linear Algebra material with a focus on applications in Sciences. This course explores abstract vector spaces, linear mappings, inner product spaces, and orthogonal diagonalization and applications.

## CALCULUS FOR ARTS AND SOCIAL SCIENCE

This first-year course is intended for students in non-STEM programs and serves as an introduction to applications of calculus in business, the behavioural sciences, and the social sciences.

## CALCULUS III

Calculus III completes a typical Calculus series and covers multivariable calculus. It assumes a good knowledge of one-variable calculus as well as the fundamentals of linear algebra. This course is intended for Math majors and is focused on theory and proofs.

## CLASSICAL ALGEBRA FOR HONOURS MATH

This is a first-year Algebra course centered on proof, the defining property of Mathematics. The course provides an introduction to the language of mathematics and proof techniques through a study of the basic algebraic systems of mathematics.

## LINEAR ALGEBRA I

Linear Algebra I covers most of a typical first year Linear Algebra course with a focus on applications in Sciences. This course explores systems of linear equations, matrix algebra, determinants, and introduces vector spaces and their applications.

## INTRODUCTORY STATISTICS

Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The course assumes some knowledge of intermediate algebra and focuses on statistics application over theory.

## INTRODUCTION TO FINANCIAL MATHEMATICS

In this course students will learn the theory of rates of interest and discount; annuities and sinking funds with practical applications to mortgage and bond questions; yield rates.

## DEVELOPMENTAL AND INTERMEDIATE ALGEBRA

This course is best suited as a Foundations of Mathematics course often taught in post-secondary institutions, covering four modules on Algebra and Geometry core principles. This course serves as an excellent prerequisite to first year college or university level Algebra and Geometry.

## PHYSICS: MECHANICS, WAVES, AND ACOUSTICS

Physics: Mechanics, Waves and Acoustics is an introductory undergraduate course that covers mechanics, sound, oscillations, and waves. This course emphasizes connections between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigour inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.

## PRECALCULUS

Precalculus is a comprehensive course that covers more ground than a typical one- or two-semester college-level precalculus course. The content is organized by clearly-defined learning objectives and includes worked examples that demonstrate problem-solving approaches in an accessible way.

## INTRODUCTION TO DIFFERENTIAL EQUATIONS

This course in differential equations covers standard approaches to solving first order ordinary differential equations along with associated qualitative analyses, second order linear differential equations and systems of differential equations. Examples and applications are drawn from the sciences and engineering.

## PROBLEM SOLVING AND MATHEMATICAL DISCOVERY

Students can learn about roughly a dozen problem techniques (such as, “draw a useful diagram”, “find a pattern”, and consider cases) and explicitly look at problem solving in a number of major topic areas (such as Number Theory, Counting, and Geometry).

## CALCULUS AND VECTORS

This material highlights derivatives of polynomial, rational, exponential, logarithmic, trigonometric functions, integral calculus, real-world applications, vectors, lines, and planes.

## CALCULUS FOR THE SCIENCES

This course in differential and integral calculus begins with a review of functions, introduces limits and explores the derivative both from a limit-based and rule-based approach, covering elementary functions and applications. Integration is introduced from the perspective of anti-differentiation, followed by coverage of Riemann sums and the Fundamental Theorems, definite and indefinite integrals and solution techniques. Arc length, area and volume integrals and other applications are introduced. Series and convergence are explored, followed by an introduction to differential equations. Finally, parametric curves and polar coordinates, and the basics of multivariable calculus are presented. Examples are drawn from applications in the sciences.

## EUCLIDEAN GEOMETRY

This course is designed to support instructors who are teaching elements of Euclidean geometry, from properties of triangles and circles to applications. The material is designed around building problem solving and proof skills.

## COLLEGE ALGEBRA

College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

This course extends students' experience with functions. Students can investigate the properties of polynomial, rational, exponential, logarithmic, trigonometric and radical functions; develop techniques for combining functions; broaden their understanding of rates of change; and develop facility in applying these concepts and skills.

## ALGEBRA AND TRIGONOMETRY

Algebra and Trigonometry provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra and trigonometry course. Algebra and Trigonometry offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

## EXPONENTIAL AND TRIGONOMETRIC FUNCTIONS

Students will be presented with course material that encompasses exponential and sinusoidal functions, properties, transformations, and applications.

## INTRODUCTION TO FUNCTIONS

Students will experience a firm foundation in functions while exploring function notation, domain and range, transformations of functions, inverses of functions, inequalities, absolute values, and reciprocals.

## LINEAR RELATIONS AND ANALYTIC GEOMETRY

Course material that is comprised of lessons relating to linear and non-linear relations, solving linear equations and linear systems, analytic geometry, and statistics.

## MEASUREMENT, GEOMETRY, AND TRIGONOMETRY

This content pack includes course modules for students that cover the Pythagorean theorem, measurement of 2D figures and 3D solids, optimization, geometric relationships, triangle trigonometry, angles in standard position, and trigonometric identities.

## NUMBER SENSE AND ALGEBRAIC EXPRESSIONS

This course material provides students with lessons to learn about exponent laws, manipulating expressions including polynomials, radical and rational expressions, and investigating prime factorization.

## NUMBERS, GEOMETRY, ALGEBRA, AND DATA

Pre-built lessons that cover negative numbers and fractions, basic algebra through patterning, proportional reasoning, and other topics, polygons, circles, and triangles.

These lessons cover graphs and tables, standard, factored and vertex forms, algebra of quadratic relations, quadratic equations, and intersections of lines and parabolas.

## SEQUENCES, SERIES, AND FINANCIAL LITERACY

Lesson material that spans arithmetic and geometric sequences, financial applications including simple interest, compound interest, and annuities.

## CONTEMPORARY MATHEMATICS

Contemporary Mathematics provides students with real-world mathematics applications in the fields of finance, probability and statistics, graph theory, and dimensional analysis.

## TRIGONOMETRY: A UNIT CIRCLE APPROACH

This course uses the unit circle approach to learning trigonometry as this approach fits much better with the concept of functions. In addition, this approach allows most topics in trigonometry to be built upon the unit circle.

## INTRODUCTION TO CALCULUS

An introductory undergraduate course in differential and integral calculus composed of five units Limits, Derivatives, Applications of Derivatives, Integrals, and Applications of Integrals.

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