I'm doing my final year of under graduation through distance education and would be appearing for entrance tests for various graduate schools in a few weeks. I am looking for a database of algorithms/flowcharts for solving several types of general problems often encountered in these tests, giving an exhaustive list of techniques and methods available and the order in which they should be applied. Here is a good example of a flowchart for solving the general problem of
"Testing a series for convergence" https://www.math.ucdavis.edu/~egoldwyn/math21c/series_flowchart.pdf.
Another example could be this for "Testing a function for uniform continuity" (just here as an example, may contain errors).
- Try to draw the graph of the function.
- Test for Lipschitz Condition.
- Use $|f(x)-f(y)|<e$ to find a $d(e)$ such that $|x-y|<d(e) \implies |f(x)-f(y)|<e$.
- Test if a continuous extension over a closed and bounded set (compact set) exists.
- Test for points of discontinuity.
- Fix an $e$ and try to find $x$ and $y$ such that $|f(x)-f(y)|\geq e$ while $|x-y|$ can be made as small as desired.
Currently when I try to solve problems under time constrains I often miss a few methods and get stuck. Since a lot of these tests are designed to test one's speed as well as understanding, such a resource would be quite helpful to improve speed after I've understood each technique thoroughly. The syllabus is roughly the topics covered in a $3$ year undergraduate course in the following areas:
If it doesn't exist and if it would be useful to others, perhaps we can create such a collection here.