How to Pick a Topic for Historical Perspectives in Mathematics Term Paper

Most importantly, choose a topic that interests you  and stretches (threfore strengthens) you mathematcially!

Some ways to think about ideas:

A very good place to see possible broad topics and subtopics in mathematics is
The MathWorld Website by Eric Weisstein:  http://mathworld.wolfram.com/

This organizes math topics by category.  Also for each topic that you search on, it gives one or more articles on it and references for more information.
 
There are been a number of interesting accessible books written recently on historically iimportant mathematical problems  -- some are quite reasonable and used copies can be ordered online.

Also, spend sometime browsing the books that are available in P. Gilbert's collection. 

Below  are some examples of ideas.

Broad Topic:  Number Theory.  Suptopics:  The Riemann Hypothesis.   Fermat's Last Theorem.

Broad Topic:  Neural Networks and Genetic Algorithms  Subtopic:  Application to a specific problem

Broad Topic:  Graph Theory.   Subtopics:  The Map Coloring Problem.  The Traveling Salesperson Problem.

Broad Topic:   The Least Squares Problem.  Subtopics: Linearization of Nonlinear Problems.  Bezier Curves, Spline Curves, and their applications to Computer Graphics.

Broad Topic:  The Central Limit Theorem.  Subtopics:  Alternative Proofs of the Central Limit Theorem (Using Fourier Transforms).  Implications of the Central Limit Theorem.

Broad Topic:  Artificial Intelligence,  Fuzzy Logic,  Fuzzy Set Theory.

Broad Topic:  Eigenvectors and Eigenvalues.  Subtopics:  Applications to Differential Equations.  Applications to Markov Processes.

Broad Topic:  Differential Equations.  Subtopics:   Numerical methods for solving D.E.  --Variations on Euler's Method.

Broad Topic:  Taylor Series Approximations.  Subtopics:  Applications of Taylor Series Approximations.

Broad Topic: Game Theory.  Subtopics:  Zero-Sum Games.

Broad Topic:   Numerical Approximation of Integrals.  Subtopics.

Broad Topic:  Prime Numbers.  Subtopics:  Mersenne Primes

Broad Topic:  Probabilistic Algorithms.  Subtopics:   Probabilistic Algorithms applied to ...

Broad Topic:  Fractals, Dynamics and Chaos Theory.   Subtopics:  The Lorenz Attractor.
 
Broad Topic:  Numerical Methods in Linear Algebra.  Subtopics. Ill-conditioned Systems.  Singular Value Decomposition. QR Decomposition.
 
 Broad Topic:  Probability.  The Weak and Strong Law of Large Numbers.