Overview:
Understanding statistical models and quantitative procedures in psychology can be enriched by a deeper understanding of mathematics. For some of my undergraduate students this simply means revising high-school mathematics, such as basic algebra and basic probability. For research students using more sophisticated quantitative methods such as structural equation modelling, multilevel modelling, item response theory, multidimensional scaling, or any number of more advanced procedures, a deeper understanding can be obtained from learning a little more mathematics. Many of the the text books on these procedures assume a good understanding of: Algebra; Calculus; Matrix Algebra; Probability; Statistics; and Linear Models.For students wanting to acquire such a mathematical understanding, free online self-study materials are improving all the time. While working through books and doing exercises is a critical part of the learning process, it is also beneficial to hear how mathematics lecturers talk about mathematics. In this vein, I have found online full length video courses particularly useful.
The full length video courses listed at Academic Earth and Cosmo Learning are good. More videos are available through Khan Academy. The Free Science Blog also lists science and maths videos. Specifically, the following lists courses useful for researchers in psychology wanting to improve their mathematical understanding:
Algebra and Introductions
- Algebra Course 1
- Pre-calculus Algebra Course (good as a refresher of high school maths) or this one
- Mathematics Illuminated provides a motivating survey of mathematics for adult learners.
- Algebra and more by Roxanne Byrne
- course materials on basic algebra and pre-calculus
Linear Algebra
- Linear Algebra / Matrix Algebra (Gilbert Strang is a motivating lecturer),
- Differential equations and linear algebra (this one by Selwyn Hollis is particularly clear, but more advanced) or a
- more advanced presentation for computer science and engineering students (also by Gilbert Strang)
- Finite mathematics including matrices, sets, probability, and markov chains
Calculus
- Clear calculus video series (Also by Selwyn Hollis)
- Single variable calculus (from MIT)
- Calculus Life Saver Course
- multivariable calculus course from Berkeley
- multivariable calculus course from MIT
- introductory calculus course materials from the Math Page
Probability
Statistics:
- Elementary Statistics Course (access through I-tunes)
- Statistics Course
- Statistical Modeling and numerical methods (estimation, point and interval estimation, bootstrapping, monte carlo methods) and more and more again
- Cornell University - Social and Economic Data
- University of Oregon - Econometrics
