Quantitative Skills > Teaching Resources > Student Resources

# Student Resources

The geosciences require a good knowledge of quantitative skills, usually first learned in math or physics courses. These skills can quickly become rusty, half-remembered, or forgotten altogether, at which point a refresher is in order. On these pages we have gathered a selection of online resources with good reference material and quick lessons, with the hopes that it might be what an ailing petrology (or atmosphere, or ecology) student needs to get back up to speed.

## Math in a Geoscience Context

• The Math You Need, When You Need It. This website covers quantitative topics that are important in introductory geoscience courses. Each topic includes a page for the instructor, quantitative information for the students, a set of practice problems and culminates in an on-line quiz that is automatically graded and submitted to the instructor.
• Keyah Math. This project is developing a series of place-based, culturally-responsive, and technology-intensive modules in mathematical geoscience for the enhancement of undergraduate geoscience courses for Native American students.
• 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 notebook.

## General Math Sites

Below are general use sites, which cover broad ranges of information with what we find to be the best clarity, illustration, and depth. More specific topics may be browsed using the links above.

• Math2.org (Formerly "Dave's Math Tables"). This general math site offers reference material on a host of math topics, plus a math message board and links to relevant material online. The tables cover a range of math skills, from basic fraction-decimal conversion to the more advanced calculus and discrete math. The information is presented in notation form, with diagrams, graphs, and tables. The site is available in English, Spanish, and French.
• MathWorld. This is an extensive resource for students of high-level mathematics. Wolfram Research and Eric Weisstein have put together this site with the very advanced student in mind, and the focal point is the enormous resource library. Covering a wide range of math topics, such as number theory, discrete mathematics, and topology, the 10,000+ pages feature notes, diagrams, example problems, definitions of theorems, and a great deal more. Pages also include history of mathematics, terminology, and MathWorld headline news.
• S.O.S. Mathematics. Providing reference and review material on many math topics, this site also features practice exams, a message board, reference tables, and a list of recommended books. Over 2,500 pages give short lessons on algebra, trigonometry, calculus, and matrix algebra. The explanations are complete and extensive, flow well from one to the next, and include plenty of sample exercises.
• Technical Tutoring. Once a website for online, one-on-one tutoring, Technical Tutoring is now a repository of help pages developed by Phil Otken. Examples and lessons on many aspects of calculus, algebra, trigonometry, and basic chemistry. Each lesson includes a concise discussion and step-by-step intructions, formulas, and figures.
• Understanding Mathematics . This site is a study guide developed by Peter Alfeld at the University of Utah. It aims to show students what it means to understand Mathematics rather than just how to solve problems.
• E-Tutor Graphing Calculator. This webpage provides an interface where students can enter an equation and see what the graph looks like. Users are able to drag the graph with the cursor to see different parts of the range of the function.

## Basic Skills

Getting stuck on a basic skill like converting units or using the Pythagorean theorem can be more frustrating than getting confused on a higher-level concept. In sediments and stratigraphy, you may have to convert distances or measures. In mineralogy, you have to make sure you understand orders of magnitude and scientific notation. In hydrogeology or geochemistry, you might get stuck with complicated equations and polynomials. These skills are easily reviewed, if you know where to look.

• Algebra - from MathWorld. MathWorld is possibly the most extensive math reference site on the web, and is geared toward the very advanced student. The algebra index is no exception, offering reference material on mainly upper level topics. Information is also available on more basic skills such as the quadratic equation, general identities, and algebraic properties.
• 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.
• S.O.S. Mathematics - Algebra. The algebra index of the extensive S.O.S.Math site has lessons and reference material on units of conversion, complex numbers, equations, and much more. Each section features a concise review, notation, examples, and practice problems.
• The Language of Algebra. Provides a brief review of many aspects of algebraic language and use, from symbol sets and fractions to exponents and factoring. Intended as a reference for students already familiar with algebra, it is the first section of the online text Introductory Statistics: Concepts, Models, and Applications.
• Understanding Algebra. A complete introductory algebra textbook, this site covers many concepts including arithmetic, word problems, graphing and lines, equations and expressions, exponents, and polynomials. Includes a graphing applet, a prime factorization machine, and a prime number list. Brennan uses inserts to answer common questions as the lesson goes on, helping the student master new ideas. A printable version is also available on the website.

## Geometry

Using a map to figure how far sites are from each other, how large a flood region is, what the volume of a resource or pluton might be – these all require a good grasp of basic geometry. Including coordinate systems and graphs, which are relevant to almost any geoscience topic, makes a very important branch of mathematics. Use the pages below for review and reference on many geometry topics.

• 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.
• 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.
• 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, polyhedra, spheres, and quadrics.
• Measurement Formulas. A handy reference on basic geometry formulas, this site covers distance, area, perimeter, and volume. Simple, straightforward notation, no diagrams or lessons.

## Trigonometry

Trigonometry is useful when logarithms show up in your structural geology relationships, or when you have to find the angle in a particular crystal for mineralogy. Review the identities, theorems, and relationships on the pages listed here.

• Math Help Pages - Trigonometry Index - Technical Tutoring. Beginning with a general review, this site provides a good refresher on basic trig identities, functions and angles. Good diagrams for unit circle and triangle trigonometry.
• S.O.S. Mathematics - Trigonometry. The trigonometry index of S.O.S. Math features a table of trigonometric identities, lessons on functions and formulae, and a section of exercises and solutions. Topics also include the derivatives of trigonometric functions and hyperbolic trigonometry.
• Trigonometry - from MathWorld. Eric Weisstein and Wolfram Research have built up a staggering number of math reference pages, all of which have extensive notation, diagrams, and examples. The trigonometry section covers basic trigonometry, identities, and angles, and also has material on more advanced topics such as spherical trigonometry, directed angles, and surveying. As with all the MathWorld sites, the information is abstracted and presented with the very advanced student in mind.

## Statistics

Geoscience research frequently results in and depends on large data sets. A grounding in statistical practice is crucial for a geoscience student to be able to manipulate and interpret their data. Whether the data come from readings off a stream gage, structural feature orientations recorded in the field, or sizes and types of grains found in a well core, use these pages as references when analyzing data.

For help with data analysis, including analysis of variance, experimental design and hypothesis testing, distributions, sampling, and curve fitting, look through the pages below.

• 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.
• Introductory Statistics: Concepts, Models, and Applications. This complete textbook covers introductory statistics in nearly 30 chapters, from algebra through critical values. The goal is to develop the concept of creating mathematical models of the world and the use of hypothesis testing as a process of verifying those models. Each chapter is presented in sections, with diagrams, graphs, tables, and extensive notation. Some exercises are offered which use SPSS/WIN 7.0.
• Probability and Statistics - from MathWorld. This site hosts a wealth of reference information on probability and statistics, from basic history and definitions to advanced applications. Topics covered include basic probability, various types of analysis, regression, distributions, and more. As with all the MathWorld sites, these have excellent notes and diagrams, but are designed for the very advanced student.

## Calculus

Geoscience uses calculus in many upper-level classes. Derivatives are important for determining rates: decay in petrology, flow in hydrogeology, sedimentation in sediments and stratigraphy. Integrals can help determine sediment accumulation, vectors are applicable to structures such as faults, and matrices come in useful in atmospheric or structural geology. They're not always the most intuitive of skills, so use a reference like the pages below.

• 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.
• 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 modules link to a MathHelp page for explanation of techniques used, and then come back to the geologic scenario to finish the problem.
• 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.
• Math Help Pages - Calculus Index - Technical Tutoring. This site features a menu of lessons and reference material on calculus concepts. Featured are several definitions of the derivative, treatments of discontinuity, and discussion of logarithms, integration, and antiderivatives. The sections are presented with clear notation and examples.
• Topics in Calculus. This page emphasizes the practical concepts of calculus, and is intended to provide a new context for the student already familiar with much of the material. The emphasis is on how calculus can actually be used outside of the classroom, and how the language of calculus is important in many other disciplines. It features articles for download, on topics from exponential growth and decay to discontinuities, vector fields and differential equations. All of the articles include extensive notes, examples, and figures.

## Linear Algebra

Systems of equation, matrices, and other topics that frequently fall under the class name linear algebra can be extremely useful when dealing with complicated geologic or atmospheric systems. Review linear transformations, eigenvalues, and more on the pages below.

• 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.
• Linear Algebra - from MathWorld. From Lie theory to matrices, this site covers most of the topics included in linear algebra. Thorough notation and diagrams enhance the review pages and clarify the theorem explanations. Topics include linear transformation, systems of equations, and a complete overview of terms and definitions. Eigenvalues and eigenvectors, as well as many relevant theorems, can be found under the matrices tab. As with all the MathWorld sites, the information is abstracted and intended for the very advanced student.
• S.O.S. Mathematics - Matrix Algebra. The matrix algebra index begins with applications and properties of matrices, works through systems of linear equations, explains determinants (including Cramer's Rule), and finishes with lessons on eigenvalues and eigenvectors. Each section includes an introduction to the topic and example problems as well as notes, tables and diagrams.