A Problem Course in Mathematical Logic

A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Mo

A First Course in Linear Algebra

A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, det

A Computational Introduction to Number Theory and Algebra

A book introducing basic concepts from computational number theory and algebra, including all the necessary mathematical background.

Atoms to X-rays: How Do Proteins Fold? Theory Meets Experiments

The machinery of life depends on proteins--large organic molecules composed of tens, hundreds or even thousands of amino acids bound together and folded into specifically shaped structures. How they fold into these three-dimensional structures is known as the second genetic code and is one of great challenges in science today. Join UCSD biophysicist Jose Onuchic, as he explores how physics, chemistry, biology and mathematics are all being applied to crack the protein folding mystery. Series: Ato

Geometry - from MathWorld

Another extensive reference site from MathWorld, this index offers pages on advanced and basic skills alike, though the information is presented with the very advanced student in mind. Very good notes and diagrams accompany reference material for plane geometry, non-Euclidean geometry, and general geometry, among many others. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/

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 - Revision Topics

This site, part of the University College London's GeoMath site, provides a review of basic math skills, including basic equations and functions, areas and volumes, and coordinates and graphs. The notation is linked throughout to a glossary of terms, and several examples are geologically based and have realistic scenarios. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/

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/

GeoMaths - 1st Level Modules

University of College London hosts a site of notation and reference material on math skills in the context of geoscience. These exercises provide realistic geologic scenarios and work through examples, with notation on the math used to solve them. Examples include using trigonometry to find the true width of strata, logarithms to understand the Richter scale, and vectors to find plate velocities at a triple junction. Relevant vocabulary is linked to a glossary of mathematical terms. Many of the

Functions of 2 Variables: Partial Derivatives

Brandeis hosts several pages demonstrating the involvement of calculus in biology. This site gives a short explanation of the partial derivative of two variables, using illustrations and various levels of magnification to demonstrate. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/

Calculus - from MathWorld

MathWorld again provides a broad range of topics, this time under its calculus index, with subjects ranging from limits to differential equations. General calculus, continuity, maxima and minima, and integrals are all covered, with lots of notes, diagrams, and examples. Many cross-references and lists of relevant texts provide a well-rounded and thorough reference for the curious and demanding student. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http:

Algebra.help - Simplifying expressions/equations with exponents

Follow this lesson to review basic exponent manipulation. Worksheets, further lessons, and lists of resources are also available. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/

Algebra - from MathWorld

Definition of the term “algebra” and examples of various “algebras”.

Hip Math and Shape Art

This lesson builds upon student knowledge of basic geometric shapes by studying the art in the illustrations shown in the video. Students draw and name organic, non-geometric shapes.

Estimation and Your TV Diet

Students develop their estimation skills while evaluating their television-watching habits and draw conclusions about the influence of television in their lives.

In math, "elegant" means "cool!"

An elegant solution to a math problem is one that requires less time and work. Encouraging students to find such solutions will help them build number sense or numeracy.

Helping parents understand

The more ongoing, positive communication you have with parents, the more they'll be willing to work with you.

Grouping skills for mastery

Thematic planning helps relate mathematics to students' lives.

Assessing the learning process

Assessment, like instruction, needs to be geared toward various learning styles, and teachers can create rubrics for ongoing assessment that keep a formal daily record of what students are learning. Traditional styles of teaching focus almost exclusively on auditory presentation of material to students — in other words, lecturing. K–12 education is moving away from that traditional model towards methods of teaching that address children’s multiple intelligences and are appropriate to diffe