# What is Highest Math Used in Social Sciences?

1. Dec 19, 2014

### bballwaterboy

I'm guessing it differs depending on the particular social science, but I'm just curious what level and types of math are used in the social science fields in general?

I do know that statistics (which I'll be taking this summer at my community college) are very common in economics and sociology. But, other than that, what other maths are used and to what level would people in these fields need to be trained? Thanks.

2. Dec 19, 2014

### Bystander

History is a social science. People study the history of science, the history of mathematics --- the history of math? Wonder how much math.

3. Dec 19, 2014

### Pythagorean

It depends on the approach. Dynamical systems theory has been used to analyze the arms race:

and of course, statistics is used for analyzing empirical data.

4. Dec 20, 2014

### FactChecker

I'll show my bias. I believe that modeling almost anything of interest has aspects of feedback systems, randomness, and optimization. Being good at those probably requires the level equivalent to advanced undergraduate or graduate. But I am sure that a lot of interesting Social Science is done without those, by people a lot smarter than me. For one thing, understanding the real situation that should be modeled takes a lot of work.

5. Dec 21, 2014

### enorbet

According to Wired, Harper's, The Globe and Mail, SiliconANGLE, Yahoo News, Medium.com Al Jazeera, Forbes, The Telegraph, and others, there is an actual "movement" occurring in Social Sciences, and so much so that referring to it as merely Social Science is something akin to describing a 3 dimensional event with only 2 dimensional terminology. There is a very good article entitled "Come With Us if You Want to Live" by Sam Frank that has been appearing since 2012 but the article is dynamic in that it is still evolving to this day so what you saw in 2012 has been substantially updated and modified as time goes on even though it appears under the same title.

This movement employs Bayesian Mathematics, Turing Completeness (eg: Lambda Calculus) , and many different computer languages such as C++, Go, Python, Javascript, etc. in constant feedback loops in OpenSource Code so that it not only continues to evolve but gather influence and scope more rapidly.

At it's beginning it was dismissed as neurotic pipe dreams but as you can see by the list above it is gathering serious attention and consideration. While it may attract some very bright but unstable characters, it's self-correcting nature tends to mitigate their influence, weeding out some who prefer the fringes and see "going legit" as some kind of "sellout". In some ways this is actually literal since the movement has individuals who are financing their research and publications through a currency similar to BitCoin.

One active aspect of this finance involves a sort of contract, one example of which is https://www.ethereum.org/. Note that the founder of Etherium, Vitalik Buterin, received the World Technology Award of 2014 beating out Mark Zuckerberg, Prime Mover of Facebook. One controversial contributor is http://lesswrong.com/about/.

I am not pointing this "movement" out with any endorsement or accolades, but rather just noting a systemic increase in applied mathematics in Social Science that is likely to continue to gather momentum rather than to fade away in order to give you something to consider in answering the question posed by this thread. There is still woo-woo a-plenty but it seems that data-mining has some similarities to actual mineral mining which these days consists largely of "upgrading ore".

6. Dec 21, 2014

### robphy

7. Dec 21, 2014

### Matterwave

The math used in finance (esp academic study of finance) can actually be quite high level. E.g. Ito (or Stratanovich) Stochastic Calculus are used to model stock markets

8. Dec 21, 2014

### Pythagorean

How successful is Stochastic Calc in finances for making predictions? I thought it had more to do with generating unpredictable motion when you're moving a lot of volume (like big companies do).

9. Dec 21, 2014

### Baluncore

The social sciences tend to discuss groups or classifications.
That would suggest that cluster analysis should be of fundamental importance.

10. Dec 22, 2014

### Matterwave

As far as I know, it's a purely academic pursuit. Predicting the stock market is of course beyond anybody's reach haha.

11. Apr 21, 2015

### wigglywoogly

People into neural networks deal with cluster analysis. And that might include cognitive scientists, philosophers, linguists.

12. Apr 21, 2015

### wigglywoogly

Here's a paper with some theory and evaluation of stock market time series methods that go beyond Ito calculus. More for (hopefully) reliable estimates of risk than for predicting the future value.
http://www.mitpressjournals.org/doi/abs/10.1162/003465302320259420#.VTbqiFkoa2w

13. Jul 27, 2015

### BWV

No one in finance uses stochastic calculus because they believe it predicts anything or it is a complete model. SC is used because it delivers workable closed form solutions that are close enough to reality to develop asset pricing models. BTW, one can add a poisson jump process to geometric brownian motion and generate non-normal, fat tailed behavior that nonetheless generates closed form solutions to SDEs

14. Feb 22, 2016

### AgentSmith

Economics is highly mathematical. Linear algebra, differential equations, Bayesian probability, numerical analysis, difference equations, and game theory are just some of the mathematics used by economists.
Geography can use advanced math. There is a journal called Mathematical Geography. Tensor algebra and topology underly map projections and are used to make new ones.

15. Feb 22, 2016

### Sophia

Philosophers are required to pass a basic logic course.
Sociology, psychology and politology require statistics.
I studied anthropology and we didn't have any math at all. That's one of the reasons I chose it :-)

16. Feb 22, 2016

### Student100

17. Feb 22, 2016

### StatGuy2000

The amount of math used in the social sciences varies substantially, from highly mathematical (economics, geography, some branches of psychology and sociology) to very little math at all (most areas of anthropology, sociology, etc.).

In terms of what types of math is used, as an example, economics uses -- among others -- statistics, probability (and not just Bayesian probability), topology, game theory, functional analysis, differential equations. I'm also aware that advanced mathematical and computational methods have been applied in psychology to model cognitive processes (this research would be closely tied to research in neuroscience and AI/machine learning).

In sociology, there has been the work of Duncan Watts (a physicist turned sociologist) whose research is in the area of mathematical models for social networks.

http://research.microsoft.com/en-us/people/duncan/