Document:CMU-MSCF-essay2

Li Quan Khoo	li.khoo.11@ucl.ac.uk	changtau2005@gmail.com
	http://lqkhoo.com/wiki	https://github.com/lqkhoo
	http://www.linkedin.com/pub/li-quan-khoo/89/a27/8aa

I'm applying for the MSCF programme right after graduating with an MEng in Computer Science. The core of the degree should be similar to other CompSci degrees, including object-oriented and functional programming, databases, algorithms, complexity, etc. The full list of subjects is in the transcript included with my application. I have mostly programmed in Python, C#, and Java in production and research code. I have written C and C++ in some capacity, but mostly in security, OS, and networking coursework. My focus during the 3rd and 4th years of the degree was on machine learning, data mining, and to some degree, natural language processing, so I am familiar with frameworks like scikit-learn and NLTK for Python, CMU's own TweetNLP, and datasets related to those areas. I have experience with regression classification methods, support vector machines, and variants, like logistic regression, regularization, or with kernels, dimensional reduction methods like PCA, and unsupervised learning methods, like k-means clustering. I have some understanding about neural network variants, and probabilistic graphical models, such as Bayes nets and Markov models, but I have not formally studied them during the degree.

The MEng degree was not mathematics-heavy; we had two units of applied mathematics, which were mostly a mix of topics required to work with computer science, like basic number theory (enough for textbook RSA), some statistics, combinatorics, zero/first-order logic, and linear algebra. Here is a more detailed list pulled directly from the syllabus: Set theoretic notation. Relations, in particular equivalence relations. Injections, surjections, bijections and their inverses. Cardinality of sets. The symmetry group, disjoint cycle notation; the sign of a permutation. Abstract groups and Lagrange’s Theorem. Euclid’s algorithm, solving linear congruences, Fermat’s little theorem, the Euler totient function, application to public key cryptography. Linear algebra. The correspondence between linear maps and matrices. Associativity and non-commutativity of matrix manipulation, Gaussian elimination. LU decomposition. Inverting matrices. Determinants. Eigenvalues and eigenvectors. Diagonalizing matrices and calculating polynomials in diagonalizing matrices. Singular value decomposition.

I have not had formal financial training - my understanding is roughly at the level of introductory textbooks to the subject, such as Principles of Corporate Finance (Richard A. Brealy et al., McGraw-Hill), and The Basics of Finance (Frank J. Fabozzi, Wiley). I am fairly confident with fundamental concepts like stocks, bonds, calls, puts, futures, long and short positions, market spread, depth, (continuous) interest rates, present value, equity, leverage, etc. - it was enough to participate in events and a hackathon run by J.P. Morgan, although to be fair, they were recruiting for software engineers at the time. I have not covered more advanced topics, like constructing an efficient portfolio, CAPM, or modelling financial time series with random processes, and models built on random walk assumptions, like the Black-Scholes model, but I would expect to learn about those during the MSCF programme.

I have been studying specifically for the MSCF programme (and other similar programmes I am applying to) since my most recent employment (August 2015), by going through lecture and coursework material available on the public domain, primarily on MIT OpenCourseware (OCW) and Coursera. At time of application, I have reviewed / covered:

• 18-01 Single variable calculus (OCW)
• 18-02 Multivariable calculus (OCW)
• 18-03 Differential equations (OCW)
• 18-06 Linear algebra (OCW)
• 6-041 Probabilistic systems analysis & applied probability (OCW)
• Financial markets (Coursera: Yale)

I found these to be quite useful in understanding at least some machine learning literature. On probability, I have covered both discrete and continuous probability density functions (marginal, joint, derived distributions), the properties of random arrival processes, specifically the Bernoulli and Poisson processes, Markov chains, and statistical inference. I have not studied stochastic calculus or partial differential equations at time of application.

I am on track (and aim) to cover at least the following before the start of the course:

• Finance (Khan Academy)
• 14-01 Principles of Microeconomics (OCW)
• 15-401 Finance Theory I (OCW)
• 18-S096 Topics in Mathematics with Applications in Finance (OCW)
• 6-262 Discrete Stochastic Processes (OCW)
• Probabilistic Graphical Models (Coursera: Stanford)