Middle School Portal: Math and Science Pathways (MSP2)
With this online activity, students explore the classic mathematics map-coloring question known as the four-color problem. Students must determine the minimum number of colors needed to color a map so that entities sharing a border have different colors. Initially, students investigate the minimum number of colors necessary to color a map of states west of the Mississippi River. The activity's Getting Started section suggests coloring the states in a specific order. The Solution page uses odd an
Middle School Portal: Math and Science Pathways (MSP2)
This online activity offers students a chance to apply the concept of symmetry to a real archaeology question. The activity calls for a hands-on solution to the initial challenge of determining the size of a plate from only a fragment or shard. Related math questions offer the opportunity to think about lines of symmetry for a variety of shapes. The activity is one of 80 mathematical challenges featured on the Figure This! web site, where real-world uses of mathematics are emphasized. The activi
Profit or loss?
This online activity challenges students to think about money and profit as they consider buying and selling a Beanie Baby. The activity is one of 80 mathematical challenges featured on the Figure This! web site emphasizing real-world uses of mathematics. After determining the profit for two transactions involving a Beanie Baby, students are asked to determine the number of attendees necessary to make a profit for a dance and to find the profit from buying and selling stock. Information about th
Middle School Portal: Math and Science Pathways (MSP2)
In this activity, students are asked to decide which would melt faster: a large block of ice or the same block cut into three cubes. The activity is one of 80 mathematical challenges featured on the FigureThis! web site. The animated introduction to this activity notes that surface area and volume are important to the work of architects, interior designers, and chemists. Students are encouraged to compare the surface area of the ice cubes to the larger block. The complete solution demonstrates h
Middle School Portal: Math and Science Pathways (MSP2)
This activity opens with a cartoon in which two characters present students with directions for arriving at a special number. Students then correlate their special number with a letter of the alphabet and choose a color that begins with that letter. The characters bet that the color is yellow, and students are challenged to discover why the bet would be correct. The activity is one of 80 mathematical challenges featured on the Figure This! web site. It introduces algebraic procedures and notes t
Tan, don't burn : how long before you burn?
This online activity offers students the opportunity to reason with numbers as they examine the practical implications of sun protection factor (SPF) numbers on sunblock. The activity is part of the Figure This! collection of 80 online mathematical challenges emphasizing real-world uses of mathematics. In this activity, the Hint and Getting Started sections illustrate how to apply mathematical reasoning. They demonstrate how to think through the answer to the initial question about how a person
Sand pictures : what's missing?
This activity opens with pictures of traditional African sand paintings called sonas. A sona is comprised of dots and loops. One design is missing, and students are asked to study the patterns and determine the appearance of the missing design. The activity, part of the Figure This! collection of 80 math challenges emphasizing real world math, explains the importance of mathematical patterns in archaeology and cultural anthropology. The Hint suggests that students examine the number and arrangem
Middle School Portal: Math and Science Pathways (MSP2)
In this activity, students explore what percentage means when looking at election results. The activity is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. The activity features questions designed to help students think carefully about how percentages are used mathematically to determine outcomes. The answer to the first question provides a detailed examination of election results. The importance of understanding the meaning of
Combination locks : I forgot the combination! How many combinations will I have to try?
This activity asks the student to find the number of possible combinations for a lock showing the numbers 0 to 39. It is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. The solution to the combination question applies the technique of using a smaller number of possible arrangements to study a problem. Students learn to use a tree diagram to model possible outcomes and explore the mathematical meaning of the term combination. Th
Middle School Portal: Math and Science Pathways (MSP2)
In this activity, students learn about the body mass index (BMI) formula and how it can be used to determine health risk. The activity is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. The activity web page contains links to a solution hint, the solution, and to other math questions, such as how the BMI formula can be written to show weight in kilograms and height in centimeters. Students and their families are challenged to u
I win! : she always wins, it's not fair!
In this activity, students play a game and examine what it means for a game to be fair. The activity is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. In the game's 12 rounds, two six-sided die are rolled, the face values are subtracted, and data are recorded on a table. Player A wins if the difference is 0, 1, or 2, and Player B wins when the difference is 3, 4, or 5. The page contains a solution hint, the solution, and relat
Middle School Portal: Math and Science Pathways (MSP2)
This activity challenges students to think about angles as geometric shapes and to find the sizes of the angles between their fingers. It is part of the Figure This! collection of 80 online mathematical challenges emphasizing real world uses of mathematics. For this challenge, the students trace a hand stretched to form an L-shape with the thumb and sketches angles of 90 degrees and 45 degrees between the thumb and index finger. They use the sketches to estimate the angles between their other fi
Middle School Portal: Math and Science Pathways (MSP2)
This web site contains descriptions and links to more than 60 virtual manipulatives, activities designed to function as concept tutorials. The virtual manipulatives, mostly in the form of Java applets, are designed to facilitate grades 6-8 mathematics learning. By encouraging active student exploration with computers, the virtual manipulatives can help students visualize mathematical relationships. They are organized into five categories based on the National Council of Teachers of Mathematics (
Logic for Computer Science: Foundations of Automatic Theorem Proving
This book is intended as an introduction to mathematical logic, with an emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. This book is designed primarily for computer scientists, and more generally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. The book is self contained, and the level corresponds to senior undergraduates and first year graduate students. However,
Mathematical Biology
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.
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.
