Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.

This lesson unit is intended to help assess how well students are able to interpret and use scale drawings to plan a garden layout. This involves using proportional reasoning and metric units.

Students act as Mars exploratory rover engineers, designing, building and displaying their edible rovers to a design review. To begin, they evaluate rover equipment and material options to determine which parts might fit in their given NASA budget. With provided parts and material lists, teams analyze their design options and use their findings to design their rovers.

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential function where C>0 and k is an arbitrarily fixed value in f(x)=Ce^(kx).

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k>0 and C is an arbitrarily fixed value in f(x)=Ce^(kx).

It is essential to lay a solid foundation in mathematics if a student is to be competitive in today's global market. The importance of algebra, in particular, cannot be overstated, as it is the basis of all mathematical modeling used in applications found in all disciplines. Traditionally, the study of algebra is separated into a two parts, elementary algebra and intermediate algebra. This textbook, Elementary Algebra, is the first part, written in a clear and concise manner, making no assumption of prior algebra experience. It carefully guides students from the basics to the more advanced techniques required to be successful in the next course.

Elementary Algebra is designed to meet the scope and sequence requirements of a one-semester elementary algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.

Complete set of mobile friendly Elementary Algebra sample exams with solutions. In addition, there are links to pdf versions and a sample final exam with answers.

This workbook was originally created by mathematics instructors at Scottsdale Community College in Scottsdale, Arizona. Jennifer Nohai-Seaman has edited their version to fit the needs of the students and professors at Housatonic Community College. It is designed to lead students through Elementary Algebra and to help them develop a deep understanding of the concepts. Special thanks to the Developmental Studies Department at Housatonic Community College and the Math Department at Middlesex Community College for their valuable and immeasurable input.

This textbook covers calculus of a single variable, suitable for a year-long (or two-semester) course. Chapters 1-5 cover Calculus I, while Chapters 6-9 cover Calculus II. The book is designed for students who have completed courses in high-school algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but the old idea of an infinitesimal is resurrected, owing to its usefulness (especially in the sciences).

- KS3 lower level algebra introduction
- Inverse operations
- algebraic equations

Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.

Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.

This task asks students to use inverse operations to solve the equations for the unknown variable, or for the designated variable if there is more than one. Two of the equations are of physical significance and are examples of Ohm's Law and Newton's Law of Universal Gravitation.

The purpose of this task is to directly address a common misconception held by many students who are learning to solve equations. Because a frequent strategy for solving an equation with fractions is to multiply both sides by a common denominator (so all the coefficients are integers), students often forget why this is an "allowable" move in an equation and try to apply the same strategy when they see an expression.

This is a standard problem phrased in a non-standard way. Rather than asking students to perform an operation, expanding, it expects them to choose the operation for themselves in response to a question about structure. The problem aligns with A-SSE.2 because it requires students to see the factored form as a product of sums, to which the distributive law can be applied.

t is increasingly clear that the shapes of reality – whether of the natural world, or of the built environment – are in some profound sense mathematical. Therefore it would benefit students and educated adults to understand what makes mathematics itself ‘tick’, and to appreciate why its shapes, patterns and formulae provide us with precisely the language we need to make sense of the world around us. The second part of this challenge may require some specialist experience, but the authors of this book concentrate on the first part, and explore the extent to which elementary mathematics allows us all to understand something of the nature of mathematics from the inside.

The Essence of Mathematics consists of a sequence of 270 problems – with commentary and full solutions. The reader is assumed to have a reasonable grasp of school mathematics. More importantly, s/he should want to understand something of mathematics beyond the classroom, and be willing to engage with (and to reflect upon) challenging problems that highlight the essence of the discipline.

The book consists of six chapters of increasing sophistication (Mental Skills; Arithmetic; Word Problems; Algebra; Geometry; Infinity), with interleaved commentary. The content will appeal to students considering further study of mathematics at university, teachers of mathematics at age 14-18, and anyone who wants to see what this kind of elementary content has to tell us about how mathematics really works.

This simulation allows you to use a slider to see how positive and negative integers add on a number line.

This seminar will teach you about special types of exponential functions that model growth and decay. You will learn how to distinguish between the two types of functions and also what types of situations are represented by each. You will learn why the specific values in each type of function have the effect on them that they do, and why the terms “growth” and “decay” are appropriate to describe the types of functions. You will see examples of each type of function and why the specific numbers in the functions have the effects of either making the values grow or decay.  StandardsCC.2.1.HS.F.1 Apply and extend the properties of exponents to solve problems with rational exponents.