Tips on Reading Mathematics for the Non-Mathematician 0comments
published in 2010-01-14 16:03:00
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This post provides a few tips on reading a mathematics text book or other mathematical material such like a journal article that includes mathematics. In particular I wrote this post for social s ...
This post provides a few tips on reading a mathematics text book or other mathematical material such like a journal article that includes mathematics. In particular I wrote this post for social science researchers with less training in mathematics except who are otherwise motivated to study mathematical material. It also offers useful li
Choosing a Text Book
Students studying a mathematics subjects are typically prescribed a text book. However for independent social science researchers the required book is often less clear. Common scenarios include: (a) you are reading a journal article and it uses a mathematical or statistical technology and you want to learn more about it; (b) you are considering applying a technique in a research project and want to learn more; or (c) you are doing a statistics course that smooths through some of the details on implementation and you want to understand these details. When choosing a text book relevance clarity and an appropriate level of sophisticated is required.
Relevance: Does the chosen book align with your learning goals? Does it go into the appropriate degree of depth for your needs?
Clarity of presentation: Some books are just better than others. Also some may be written with your particular applications and concerns in mind. For sample there are many mathematics books written with the social scientist in mind. They often make fewer assumptions about background mathematical scholarship and present relevant applications.
The right level of sophistication: This depends on your prior knowledge. Most mathematics textbooks will list the assumed knowledge in the preface or in an introduction. Failing that a seem at the first few pages will tend to reveal whether the book is as well sophisticated.
If a book is too sophisticated you are confronted with the selection of whether it is worth acquiring the prerequisites to understand it. If you determine the book is worth reading you must then ascertain what such prerequisites are and job out a means of acquiring them. This assumes some knowledge of the hierarchical dependencies between mathematical topics. I have previously posted on this in relation to a sequence of videos and textbooks related to learning statistics. A knowledgeable adviser can also assist in setting a sequence of self-study.
Once a textbook has been selected there is the question of how to read the material in order to obtain the desired skills and knowledge.
Active Reading
Reading mathematics is different to reading other material. The following are a concise set of suggestions. The subsequent li
read with a pen and paperdo provided problemscreate problems and do themwork slowly monitoring comprehensionstructure the material; recognize core concepts and interrelationshipsidentify material that is not understood and conceive methods to learn itlearn to read the symbols: Learn how to pronounce the symbols: I previously posted on li
Additional Online Resources
The following li
Kevin Lee: List of tips for reading mathematics textbooksSteven Diaz: Short and sweet set of slides on reading mathematics.Angela Vierling-Claasen: Guide including structured questions to beg yourself while reading mathematical material and some strategies for what to do when a hardship is encountered.Shai Simonson and Fernando Gouvea: Material on how to read mathematics. They advise to see the large picture be an energetic reader read slowly and make the ideas your own. They make several analogies between the specialised skills of reading mathematics and those of reading fiction poetry and non-fiction. They also provide an example of applying their advice.College-algebra: Tips on reading a mathematics textbookStephen Maurer: Advice for Undergraduates on Special Aspects of Writing Mathematics is more about writing mathematics than reading. However it is also helpful in accord some of the conventions of mathematical discourse.Oklahoma State University: How to Read Mathematics for Meaning – Making Sense of Mathematical Prose. This has some tips with further li
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