Pooya Taherkhani

Here I present a mathematical proof that I wrote while working with a team of kind and knowledgable math teachers who sparked the core idea and gave me a hint or two toward the proof!

This is a proof of the fact that the slope of a line connecting two integer points on the graph of a univariate polynomial with integer coefficients is itself an integer. This is not a trivial fact, although it might seem like it.

Here I present my iterative solution to the famous \( n \)-queens problem. I haven't seen an iterative solution anywhere else. It is not trivial to come up with one, so much as that even some heavy-weight computer scientists have settled for publishing an iterative version that solves the problem only for a fixed value of \( n \), say \( n = 4 \). You can see the implementation of my solution in Python and C here.

Here I have presented a few proofs about classical machine learning algorithms, such as perceptron, support vector machines, and their kernelized versions. I have then applied these methods to the classical problem of recognizing digits from images. The accompanying code is here; written in R, Python, C++, and Bash.

Here I wrote a relatively long proof involving vector calculus for a modified error measure of regularized linear regression. Here I implemented the derived vectorized error measure to fit a polynomial curve to given data. Vector formulas have the advantage of running fast on numerical software (such as R, NumPy, MATLAB, etc.). The implementation is in R.

Here I wrote a few proofs on machine learning methods, such as the kernel technique, \( k \)-nearest neighbors, support vector machines for regression, and optimiztion.

This is a program that I wrote to draw bounding boxes around objects in an image. Here I have described the neat object-oriented design of the program, which I really enjoyed developing. As an added bonus, I made the program run faster using multiple threads. Here you can see the code written in C. The program was developed in C to use the pthread library for multithreading.

Although C is not an object-oriented language, but nothing stops a good programmer to follow the design patterns to define abstract data types composed of other abstract data types, which makes for a smoother development process, and results in a more manageble program.

I wrote two programs to showcase my program design skills. Both programs process and analyze a relarively large dataset, without utilizing ready-to-use data analysis libraries. One is called border analytics and the other is purchase analytics. Both are written in Python by following the design patterns, to the extent possible, to create neat, manageble programs.

Here is a tutorial that I wrote while tutoring some calculus students who needed to brush up on their trigonometry skills. Although basic, you might enjoy my presentation of the geometric definition of tangent and cotangent functions, as well as the definition of \( \pi \) and radian.