Online resources
Stamash.org
The St Andrews Maths and Stats Hub at www.stamash.org has lots of resources for both maths and stats related questions. It has been developed in consultation with students to create an intuitive structure and focus material on areas of most interest to St Andrews students. You can search the hub or filter by degree subject, topic, format and software.
How to Write Maths
Dr Kevin. P. Lee has and excellent Guide to Writing Mathematics. It is written for an American audience but the points still hold.
Professor Robert Ash also has some pertinant remarks about writing maths.
Online video tutorials and practice questions
The Kahn Academy has an excellent, well curated selection of video tutorials covering all sorts of science. It has comprehensive sections for maths including:
- Basic arithmetic and algebra
- Trigonometry
- Linear Algebra
- Multivariate Calculus
- Differential Equations
and most subjects in between. There are also sections of probability and statistics which cover subjects including
- Probability
- Mean, Variance, Standard Deviation and Standard Error
- Binomial, Poisson, Normal and Exponential distributions
- Confidence intervals, t-tests and Chi-squared tests
- ANOVA. .
There is also a range of practice questions.
Online mathematical resources
A great deal of mathematical material is freely available online. For general mathematic queries try, for example:
- MathCentre provides self-study resources for a huge range of topics covering the transition from school to university.
- Maths Tutor offers Video tutorias, study material and practice questions in:
- arithmetic
- algebra
- functions & graphs, sequences & series
- geometry, vectors
- trigonometry
- differentiation
- integration
- IBVodcasting has a range of videos covering maths at the international baccalaureate level. The topics range from very basic maths to more sophisticated applications. You can browse all videos or select by level.
- Standard level covers topics including:
- trigonometry
- vectors and geometry
- logarithms and exponents
- calculus and optimisation
- sequences and series
- Higher level extends standard level topics and also includes:
- induction
- curve sketching
- binomial expansion
- polynomial division
- The BBC's GCSE bitesize website has revision tips and practice tests.
- MathWorld at Wolfram is a "comprehensive and interactive mathematics encyclopedia".
- The Math Forum at Drexel University, Philadelphia has numerous further links to online resources.
- The Encyclopaedia of Maths maintained by Springer is a comprehensive reference work encompassing both maths and stats up to post-graduate level. It is a reference work rather than a pedagogical work though so be aware that the descriptions can be quite technical.
- MacTutor at in the maths and stats department at St Andrews is an excellent resource focused on the history of maths.
- Topic Specific resources
- Elements of Abstract Algebra is an online introductory level algebra book encompassing groups, rings and Matrices but with a focus on Linear Algebra
- Analysis Webnotes is an online anlaysis course with lots of examples and proofs (note this is real analysis not complex or data analysis)
- Complex Analysis by George Cain is an online text book.
- Game Theory.net is a site devoted to Game Theory resources including a repository lecture notes, a glossary of terms and various interactive resources.
- Geometry Formulas and Facts is a useful reference document for 2 and 3 dimensional geometry
- Jim Heffron has made his Linear Algebra book available online with lots of worked examples.
- Multivariable Calculus by George Cain & James Herod (used at Georgia Tech) is an online text book.
- probability.net contains tutorials on topics in real analysis, measure theory, and general topology. Don't be fooled by the name, it aims to set up the foundations of probability theory
- Professor Robert Ash (at the University of Illinois Urbana-Champaign) has produced a number of more advanced texts including:
- Abstract Algebra is a more advanced text. It is from the U.S. so will take students from 3rd Year Undergraduate through to Masters Level Algebra.
- Algebraic Number Theory is an introduction to the subject covering global and local fields
- Commutative Algebra
- Complex Variables
- Real Variables with Basic Metric Space Topology
Online statistical resources
Jim Deacon (in the Biology Department at Edinburgh University) has produced The Really Easy Statistics Site, an excellent user-friendly guide to the basics of experimental design and to some of the common statistical tests.
The Psycbology department of East Carolina University has some very accessible tutorials in statistics using SPSS/PASW. They cover how to implement and interpret analyses as well as programmes to implement proceedures not available from the standard user interface.
Statistical Online Computational Resource has a range of resource including interactive graphics and video tutorials. The probability and statistics e-book is a useful reference for methods and definitions in probability and statistics with everything from describing data through -1 & 2-way ANOVA to Bayesian stats. It gives definitions, describes methods and shows examples but doesn't give theoretical derivations or justifications.
If you are having difficulty using SPSS or minitab, Birmingham University hosts very useful How to Guides that walk you through screenshots with step-by-step instruction on choosing and performing various statistical analyses. (Although written specifically for old versions of these packages these is still a VERY useful site). If you are still having difficulty using SPSS or minitab then you might like to consider trying the online calculator provided by Vassar College.
Please note: Free one-to-one help with any mathematics or statistics-based problem is available via the Maths Support Centre