These are my lecture notes for a course I teach on mathematical biology at the Hong Kong University of Science & Technology. My main emphasis is on mathematical modeling, with biology the sole application area.
Statistical Methods in Biomedical Imaging
This resource contains the complete materials (syllabus, class notes, assignments, web-based software analysis and visualization tools) for a semester-long upper-division or graduate course on mathematical modeling, statistical analysis and visualization of biomedical imaging data.
Missing Angle Puzzles
This lesson lays some of the ground work for eventually writing two column proofs. In the lesson students use known geometric facts to solve for missing angles. Students are asked to identify the key concepts required for the solution and to record the a path for finding the measure of a particular angle. Key concepts include the sum of the measures of the interior angles of a triangle and quadrilateral, parallel line relationships, and what can and cannot be assumed from a drawing.
Geometry Formulas and Facts
This excerpt from the CRC Standard Mathematical Tables and Formulas covers geometry, excluding differential geometry. It is a reference for advanced students, and covers the material in quick, condensed sections of notes. Notes and diagrams are organized into sections and subsections, starting with coordinate systems, plane transformations, lines, and polygons in two-dimensional geometry. The section on three-dimensional geometry covers coordinate systems in space, space symmetries, directions,
GeoMaths MathHelp Material
This site provides students with mathematics self-study material which is embedded within the context of the geosciences. The material consists of many MathHelp "notebooks" covering specific mathematical topics related to a relevant geological context, such as plate velocity or cliff erosion. The notebooks contain explanations, illustrations, and examples. A mathematical glossary is also constantly available, providing a brief explanation of mathematical keywords and links to the relevant notebo
GeoMaths - 2nd Level Modules
The highest level of math on the University College London's GeoMath site, this covers skills such as complex numbers, partial differentiation, matrices, advanced vectors, and probability. Each section features a menu of topics and links to a glossary. Many have geology-based examples, using the mathematical skill within a realistic scenario. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/
Division Races I
Practice your mental and mathematical agility with arithmetic races. A sequence of levels with timed questions. Each level gets progressively faster. The questions themselves are based on division and involve positive integers in the range 0 - 9999. There are a total of 11 levels, combing both multiple-task and single-task questions. Points available increase as the time decreases. Tracking of numerous performance measures is available for self-analysis and parental analysis.
Arithmetic Races II
Practice your mental and mathematical agility with arithmetic races. A sequence of levels with timed questions. Each level gets progressively faster. The questions themselves are based on the four main arithmetical operations (addition, subtraction, multiplication and division) and involve positive integers in the range 0 - 1000. There are a total of 11 levels, combing both multiple-task and single-task questions. Points available increase as the time decreases. Tracking of numerous performance
Applied Mathematics II
In this applied maths quiz, some children set out to complete their toy zoo. While out shopping they encounter numerous arithmetical problems involving addition, subtraction, multiplication and division of currency units. This helps your child gain the independence required to manage their own pocket money. Currencies used in the module are dollars, pounds and euros. The module includes many puzzles, involving sums of money up to about 20 to 30 dollars, euros and pounds, including calculation wi
Applied Mathematics I
The quiz is set in Ancient Egypt. A group of ancient Egyptians set about their everyday lives and encounter mathematical problems. Solve them and help them on their way to the afterlife. Seven levels of randomized applied mathematical problem are included. Randomisation and fresh generation of new material maintains a high level of replayability until the underlying skills are mastered. Tracking systems are included for parental supervision. Rewards maintain student interest.
This site is a free resource for math review material from algebra to differential equations. It provides more than 2,500 pages of short and easy-to-understand explanations for subjects including algebra, trigonometry, calculus, differential equations, complex variables, matrix algebra, and various mathematical tables. The materials on this site are designed for high school students, college students, and adult learners. Links to recommended books and other math education websites are also provi
Environmental Decision Making
Using the Extend 'connect-the-components' visual programming, students can model and simulate ecosystems including social and economic forces as well as study parameter variations to develop an understanding of ecosystem function and productivity. By making 'what if...' changes in the model, the effects of various proposed decisions about the environment can then be shown. EDM includes three ecological systems: Ponds, Grasslands, and Logging. Students can predict results of changes in the mode
When I started teaching this subject I found three kinds of texts. There were applications books that avoid proofs and cover the linear algebra only as needed for their applications. There were advanced books that assume that students can understand their elegant proofs and know how to answer the homework questions having seen only one or two examples. And, there were books that spend a good part of the semester multiplying matrices and computing determinants and then suddenly change level to wo
Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) i
Private Universe Project in Mathematics: Workshop 3. Inventing Notations
We learn how to foster and appreciate students notations for their richness and creativity. We also look at some of the possibilities that early work in creating notation systems might open up for students as they move on toward algebra.,15 min. Pizzas in the Classroom In Englewood, New Jersey, Blanche Young, who attended the summer workshop, tries out one of the problems with her fourth-grade students. Later, she meets with Arthur Powell to discuss the lesson. 5 min. New Brunswick, New Jersey
Private Universe Project in Mathematics: Workshop 1. Following Children's Ideas in Mathematics
An unprecedented long-term study conducted by researchers at Rutgers University followed the development of mathematical thinking in a randomly selected group of students for 12 yearsfrom first grade through high schoolwith surprising results. In an overview of the study, we look at some of the conditions that made the students math achievement possible.,10 min Building Towers Five-High The Kenilworth students in the fourth grade are seen working on the Towers problem (How many different
Introduction to Economic Analysis
This book presents standard intermediate microeconomics material and some material that, in the authors' view, ought to be standard but is not. Introductory economics material is integrated. Standard mathematical tools, including calculus, are used throughout. The book easily serves as an intermediate microeconomics text, and can be used for a relatively sophisticated undergraduate who has not taken a basic university course in economics. Podcast also available
Basic Analysis: Introduction to Real Analysis
This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course woul
Impact of Computer Aided Learning on Children with Specific Learning Disabilities
The Technology Initiatives Division of Azim Premji Foundation has launched programmes for use of computers in rural schooling. One such programme is Computer Aided Leaning (CAL) that envisages deployment of computers as a media to impact learning competencies and to create an attractive environment in the schools. The state government provides the computers in schools and the Foundation has developed required software content designed to aid classroom learning process in specific areas such as m
InterMath is a professional development effort designed to support teachers in becoming better mathematics educators. It focuses on building teachers' mathematical content knowledge through mathematical investigations that are supported by technology. InterMath includes a workshop component and materials to support instructors. For each of the following problems, consider how you would pose the same problem to your students. Would the wording need to change? Would you need to include more pictur