arXiv subjects
Publications and source records attributed to Marc Maliar.
In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we introduce the polynomial ring and the fundamental relationship between polynomials and sets of points. We prove some results in algebraic geometry, notably Hilbert's Basis Theorem.
I use simulation of two multilayer neural networks to gain intuition into the determinants of human learning. The first network, the teacher, is trained to achieve a high accuracy in handwritten digit recognition. The second network, the student, learns to reproduce the output of the first network. I show that learning from the teacher is more effective than learning from the data under the appropriate degree of regularization. Regularization allows the teacher to distinguish the trends and to deliver "big ideas" to the student. I also model other learning situations such as expert and novice teachers, high- and low-ability students and biased learning experience due to, e.g., poverty and trauma. The results from computer simulation accord remarkably well with finding of the modern psychological literature. The code is written in MATLAB and will be publicly available from the author's web page.