This book was designed as an introductory trigonometry textbook for college students with the explicit goal of reducing textbook costs.
In this course students will learn about Noetherian rings and modules, Hilbert basis theorem, Cayley-Hamilton theorem, integral dependence, Noether normalization, the Nullstellensatz, localization, primary decomposition, DVRs, filtrations, length, Artin rings, Hilbert polynomials, tensor products, and dimension theory.
This 4-minute video lesson introduces Khan's series on complex numbers.
This single minute video lesson looks at how to add complex numbers.
This 4-minute video lesson give an example of a complex conjugate.
This 5- minute video lesson shows how to divide complex numbers.
This 4-minute video lesson looks at the imaginary roots of negative numbers.
This 6-minute video lesson explains how to multiply complex numbers.
This 2-minute video lesson explains how to subtract complex numbers.
This resource contains activity handouts, a rubric, a facilitation guide, and tex files. The material is meant to be used for those teaching a college algebra course. The activities are meant to provide a deeper understanding (than a traditional course offers) of some of the topics covered in a college algebra course. The activities are intended for group activities and options exist for use in a single class or multiple classes.
All of the mathematics required beyond basic calculus is developed “from scratch.” Moreover, the book generally alternates between “theory” and “applications”: one or two chapters on a particular set of purely mathematical concepts are followed by one or two chapters on algorithms and applications; the mathematics provides the theoretical underpinnings for the applications, while the applications both motivate and illustrate the mathematics. Of course, this dichotomy between theory and applications is not perfectly maintained: the chapters that focus mainly on applications include the development of some of the mathematics that is specific to a particular application, and very occasionally, some of the chapters that focus mainly on mathematics include a discussion of related algorithmic ideas as well.
The mathematical material covered includes the basics of number theory (including unique factorization, congruences, the distribution of primes, and quadratic reciprocity) and of abstract algebra (including groups, rings, fields, and vector spaces). It also includes an introduction to discrete probability theory—this material is needed to properly treat the topics of probabilistic algorithms and cryptographic applications. The treatment of all these topics is more or less standard, except that the text only deals with commutative structures (i.e., abelian groups and commutative rings with unity) — this is all that is really needed for the purposes of this text, and the theory of these structures is much simpler and more transparent than that of more general, non-commutative structures.
This resource contains class notes, an activity handout, and a facilitation guide. Students play the game “Let’s Make a Deal” to explore the underlying probability that guides the optimal strategy for contestants. This activity aligns with MATH 1342 Learning Outcome 3: Compute and interpret empirical and theoretical probabilities using the rules of probabilities and combinatorics.
This 9-minute video lesson is about identifying conics.
This 6-minute video lesson looks at non-linear systems of equations.
This 7-minute video lesson concludes the look at non-linear systems of equations.
Understanding alternate coordinate systems. Created by Sal Khan.
Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined. Created by Sal Khan.
This resource contains a facilitation guide, class notes, and an activity handout. Students play the game “Let’s Make a Deal” to explore the underlying probability that guides the optimal strategy for contestants. This activity aligns with MATH 1332 Learning Outcome 4: Demonstrate fundamental probability/counting techniques and apply those techniques to solve problems.
This resource contains a slide deck and a facilitation guide. Students are guided to consider how mathematics can help us understand the phenomenon of a pandemic and inform our responses. Students work in groups using the NCTM’s browser pandemic app to manipulate four factors that influence the spread of a virus to see the how changing these variables creates different outcomes. They learn and explore how a log curve is used in this model. This activity aligns with MATH 1332 Learning Outcome 6: Demonstrate the ability to choose and analyze mathematical models to solve problems from real-world settings, including, but not limited to, personal finance, health literacy, and civic engagement
This resource contains a student activity handout, class notes, and a facilitation guide. Students work together to discover one-to-one correspondences between various infinite sets of numbers and the set of natural numbers. At the end of this activity the compiled results of their group work form a list of infinite sets that all have the same cardinality as the set of natural numbers. Instructors may take this lesson further by discussion countably infinite versus uncountably infinite sets. This activity aligns with MATH 1332 Learning Outcome 1: Apply the language and notation of sets