Mathematics

Research in Mathematics

Research in mathematics can rely solely on the analyses of the data produced by your own calculations or applications of the mathematical formulae associated with the differing mathematical disciplines. Secondary source material can be utilized to consider external proofs or approaches (for example, the application of a historical mathematical theorem on a contemporary school of mathematics). Remember that research in mathematics should concentrate on the mathematics involved in the research question and not on the history of the mathematical ideas.

Primary vs. Secondary Sources

Useful Research Resources

Our Library Services (Sign-in with Google):

Free-ish Online Resources:

We do not have subscriptions to these resources, but most offer a limited number of sources for free. If there is a source that you want and cannot access, contact your librarian. We can often find the same source through a different service.

arXiv.org (from Cornell University)
How to Use the Equation Editor in Google Docs
GeoGebra Classic - Free online apps bundle from GeoGebra: get graphing, geometry, algebra, 3D, statistics, probability, all in one tool
Quartile Calculator | Interquartile Range Calculator - Calculate first, second and third quartiles for a set of data. Find median, interquartile range IQR, dataset minimum and maximum for statistics data analysis.
Research Randomizer - A free resource to generate random numbers or assign participants to experimental conditions
MathType
PhET Interactive Simulations

Sources for Statistics:

Research Questions and Methodologies

Mathematics research is a long-term and open-ended exploration of a set of related mathematical problems that are based on personal observations. This research should be guided by analysis of primary and secondary sources. Methodological approaches may follow one of these types:

An analysis of te effectiveness or application of a given mathematical theory
An exploration of the utility of mathematics (theory or models) in other disciplines

Examples

Square–triangular numbers and Pell’s equation. How many square numbers are also triangular numbers, where are they and what other problems lead to Pell’s equation?

A description of square and triangular numbers, and how the locations of numbers that are both are solutions of Pell’s equation. Some other problems, perhaps in number theory and geometry, that lead to the equation could be described, with a brief history of the equation included.

The exponential function and the measurement of age and growth. How does the exponential function, and its calculus, inform areas of science such as nuclear physics, geology, anthropology or demography?

Use one of the settings where exponential growth applies, perhaps modeling the world’s population, to describe the phenomenon. Show how it is applicable in mathematical models of other real situations.