The aim of this session is to cover the basic theory of compact linear operators on Banach spaces. This includes definitions and statements of the background and main results, with illustrative examples and some proofs.

Target audience: This material is accessible to anyone who has a basic knowledge of metric space topology, and who knows what a bounded linear operator on a Banach space is. It is most likely to be suitable for postgraduate students or final year undergraduates.

Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.

This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers. Three sections of problems (which include exercises as well as unsolved problems) complete the text.

Introductory Statistics is intended for the one-semester introduction to statistics course for students who are not mathematics or engineering majors. It focuses on the interpretation of statistical results, especially in real world settings, and assumes that students have an understanding of intermediate algebra. In addition to end of section practice and homework sets, examples of each topic are explained step-by-step throughout the text and followed by a Try It problem that is designed as extra practice for students. This book also includes collaborative exercises and statistics labs designed to give students the opportunity to work together and explore key concepts. While the book has been built so that each chapter builds on the previous, it can be rearranged to accommodate any instructor’s particular needs.

The CyberSquad creates a bar graph representing the amount of bugs that are infecting the Cybrary in this video from Cyberchase.

In this Cyberchase video segment, the CyberSquad locates the Cyberchase Council by using negative numbers.

By Joan Garfield, Robert delMas and Andrew Zieffler, University of Minnesota What are Model-Eliciting Activities? Model-Eliciting Activities (MEAs) are activities that encourage students to invent and test models. ...

This animation from KET's distance learning physics course demonstrates the mathematical formula for a scientific law as it applies to light.

The goal of this exercise is to use triangulation to investigate bias and measurement validity in parents/teachers evaluations of student health and learning. 

This plan involves observing and labeling clouds and conducting an experiment on how clouds form.

Dominoes have become a staple in most primary classrooms. They build upon dice patterns and are often used to model decomposition of numbers, building student knowledge of addition facts. They are an excellent manipulative for primary students to use and these are some examples of how students might use dominoes in the math center. Try these domino games with students to improve math skills and number recognition. Encourage students to play these games at home with their families, using real dominoes or paper copies.

This article highlights resources that can be used to supplement lessons on extreme weather, including games and video clips. The article appears in the free, online magazine for K-Grade 5 teachers Beyond Weather and the Water Cycle. The magazine focuses on the essential principles of climate science.

After studying that iron is attracted to magnets, students will use magnets to extract food-grade iron filings from iron-fortified food.

This lab activity demonstrates the difference between stabilizing and directional natural selection using two separate populations of sunflower seeds.

This set of activities is designed to help students develop an understanding of scale/distance and ordering the planets from the sun, understanding Earth's position in the solar system, and developing new ways of determining "order."

Students will understand that projectile motion is a result of two independent motions, horizontal and vertical by reading, problem-solving, and experimentation.

This activity is a interdisciplinary field investigation where students will form observations and make calculations about stream characteristics and stream flow.

This activity is a lab investigation where students develop an investigable inquiry question, construct a fleet of boats, collect data about how many passengers (pennies) each will hold before sinking, interpret their findings, and will share methods and results during a poster session.

Spreadsheets Across the Curriculum module. Students use the Compound Interest Equation and an annuity equation to calculate the growth of investments over time.