# MATH AND STATISTICS

### Algebra 1

Algebra 1, Algebra 2, Calculus, Differential Equations, Econometrics, Geometry, Linear Algebra, Logic, Prealgebra, I have won many awards in Algebra including for first place individual speed and team awards (MathCounts) and very high awards for Math Olympiad (scoring 24/25). Since then, I have continued to stay sharp in algebra by completing coursework in Differential Equations and advanced Calculus, by tutoring students in algebra and in quantitative GRE, and of course by applying algebra to everyday life.

### Algebra 2

Algebra 1, Algebra 2, Calculus, Differential Equations, Econometrics, Geometry, Linear Algebra, Logic, Prealgebra, I have won many awards in Algebra including for first place individual speed and team awards (MathCounts) and very high awards for Math Olympiad (scoring 24/25). Since then, I have continued to stay sharp in algebra by completing coursework in Differential Equations and advanced Calculus, by tutoring students in algebra and in quantitative GRE, and of course by applying algebra to everyday life.

### Calculus

I have done coursework and earned A’s through Multivariate Calculus 3 and Differential Equations, plus additional work involving stochastic partial differential equations. I am familiar with real-world calculus and differential equation applications involving such numerical methods as binomial trees and finite difference meshes applied to financial, economic, and physical data, including force fields, densities, business unit optimization, options pricing, springs, mechanical vibrations/oscillations, population modeling with harvesting, and thermal or stock price diffusion. If you would like any help with calculus, I would be delighted to be of service.

### Differential Equations

I have done coursework and earned A’s through Differential Equations and have also earned an A in and TA-ed Applied Financial Derivatives, which involves deriving and solving the Black-Scholes-Merton stochastic partial differential equation and other stochastic differential equations related to derivatives pricing. To stay current on the latest developments, I have attended partial differential equations research conferences at the University of Chicago. Making differential equations useful, I have applied differential equations modeling to applications involving such numerical methods as binomial trees and finite difference meshes applied to financial, economic, and physical data, including force fields, densities, GDP forecasting, options pricing, the bouncing movement of springs, mechanical vibrations/oscillations, population modeling with harvesting, chemical solutions, anesthetics, and thermal and stock price diffusion. Thus, I can help you gain the understanding of differential equations you need for professions ranging from engineering and physics to economics, chemistry, medicine, and high finance. Differential equations is also one of those difficult classes in which good grades impress when you apply for admission to the most selective universities and graduate institutions. If you would like any help with Differential Equations, I would be delighted to be of service.

### Econometrics

Academically, I have completed graduate-level Time-Series Econometrics and Cross-Section Econometrics. I also have TA-ed Econometrics and used econometrics extensively in assignments and in original research (e.g. my honors thesis). Further, I have attended top-tier PhD-level conferences in which leading academics, some with Nobel prizes and eminent textbook authors (e.g. Wooldridge and Hamilton), have presented original research on the forefront of econometrics. While I can mention my econometric qualifications, students totally make my day when they write: “Great tutor, knows his material. Lewis is a tremendous tutor. He makes certain of your comprehension of the material. He sends a nice summary of the lesson after. Well worth it! Thanks Lewis.” (Masters, Time-Series Forecasting) If you would like any help with econometrics, I would be delighted to be of service.

### Geometry

In addition to introductory geometry, I have studied Calculus 3 with Analytic Geometry, which discusses many of the concepts of Geometry except in multidimensional space instead of only a 2-dimensional plane. I have also tutored geometry as preparation for graduate school entrance examinations.

### Linear Algebra

In our data-driven age, applications of linear algebra are ubiquitous. Linear algebra applies math to such matrices as any Excel spreadsheet, and using the power of matrices, you can calculate millions of values or solve billions of equations simultaneously. I have used linear algebra in such advanced math classes as Multivariate Calculus 3, Differential Equations, and graduate-level Time-Series Analysis and Cross-Section Analysis. Multivariate Calculus 3 uses the basic operations of Linear Algebra, including dot products and cross products, to calculate speeds, positions, and forces in infinite-dimensional space. Differential Equations uses linear algebra to solve high-order systems of differential equations to calculate eigenvalues and eigenvectors using Cramer’s rule. Building on Linear Algebra as a prerequisite, Time-Series Analysis begins its first week covering not matrix algebra but matrix calculus, using linear algebra to calculate a plethora of statistics, just as Cross-Section Analysis uses the linear algebra techniques of factor rotation in principal components analysis to reduce the dimensionality of correlated variables. In addition to using linear algebra in this more advanced coursework, I have also used the techniques of linear algebra professionally in calculating portfolio analysis and risk statistics in MatLab. If you would like help with Linear Algebra, I would be delighted to be of service.

### Logic

I took logic and earned an A. Since then, I have continued to study additional fallacies and have applied it in advanced philosophy (e.g. Philosophy of Mind, of Law, and of Politics) while studying abroad at the University of Oxford.

### Prealgebra

I have won many awards in Algebra including for first place individual speed and team awards (MathCounts) and very high awards for Math Olympiad (scoring 24/25). Since then, I have continued to stay sharp in algebra by completing coursework in Differential Equations and advanced Calculus, by tutoring students in algebra and in quantitative GRE, and of course by applying algebra to everyday life.

### Precalculus

I have completed coursework and earned A’s through Multivariate Calculus 3 and Differential Equations, plus additional work involving stochastic partial differential equations. I can help with all aspects of Pre-Calculus, including vector and matrix math, identifying real and complex roots (e.g. via graphs and positive real zeroes), rules of exponents and logarithms, graphing exponential and parabolic equations, identifying equations for exponential and parabolic graphs, trigonometric functions and the unit circle, arithmetic and geometric series, converting repeating decimals to fractions, probability (e.g. permutations, combinations, and conditional and independent probabilities), binomial theorem and binomial trees, and real-world applications for all of these (e.g. firing cannonballs, investment portfolios, options pricing, heat diffusion). While I can mention my mathematical qualifications, students totally make my day when they write: “Wonderful Tutor!! We highly recommend Lewis!! My son was failing pre-calculus/trigonometry before Lewis came along and his confidence was the lowest I’ve ever seen. After only 3 sessions, his grades have improved tremendously. He received a “B” on a quiz last week, and an A+ this week! Lewis provides clear explanations to a complex subject-matter through real-life examples. His passion for math is contagious!”

### Probability

Having completed six probability and statistics classes, including graduate-level Time-Series Analysis and Cross-Section Econometrics, I have tutored dozens of students on statistical concepts and helped them craft their own original statistical research projects in psychology, economics, and nursing. I have conducted original statistical research in Experimental Psychology, Government Research Methods, and Economics/Finance, including my honors thesis forecasting probabilities economic crises using international panel data. (Exceptionally complex panel data combines observations from different places and times.) Empirically, I have familiar with such graduate-level probability models as linear probability models and ordered and multinomial logits and probits and with Bayesian probability. As a TA and tutor of two Econometrics classes at the College of William and Mary, I helped dozens of students design their own research and analyze their results in STATA. For personal interest, I have advanced my statistical skills by attending academic conferences hosted by the American Statistics Association, the Econometric Society, the Society for Financial Econometrics, and STATA. Through this, I have gained familiarity with many statistical software packages (e.g. SPSS, STATA, EViews, and MATLAB) and various statistical programming languages. If you would like any help with probability, I would be delighted to be of service.

### R

In addition to completing courses in Advanced R and attending multiple annual conferences in R in Finance, my R background includes daily coding in R, including data manipulation, visualization, regression, and time-series analysis. Having helped students and working professionals at various schools and institutions in-person and online across multiple continents debug R code, I would look forward to helping you make sense of your R code too.

### Statistics

Having completed six statistics classes, including graduate-level Time-Series Analysis and Cross-Section Econometrics, I have tutored dozens of students on statistical concepts and helped them craft their own original statistical research projects. I have conducted original statistical research in Experimental Psychology, Government Research Methods, and Economics/Finance, including my honors thesis forecasting economic crises using international panel data. (Exceptionally complex panel data combines observations from different places and times.) As a TA and tutor of two Econometrics classes at the College of William and Mary and as a WyzAnt tutor, I have helped dozens of students design their own research and analyze their results in STATA. For personal interest, I have advanced my statistical skills by attending academic conferences hosted by the American Statistics Association, the Econometric Society, the Society for Financial Econometrics, and STATA and might even have met and discussed statistics with the author of your textbook. Through this, I have gained familiarity with many statistical software packages (e.g. SPSS, STATA, EViews, and MATLAB) and various statistical programming languages. While I can mention my statistical qualifications, students totally make my day when they write: “Great tutor, knows his material. Lewis is a tremendous tutor. He makes certain of your comprehension of the material. He sends a nice summary of the lesson after. Well worth it! Thanks Lewis.” (MFin, Time-Series Forecasting) If you would like any help with statistics, I would be delighted to be of service.

### Trigonometry

I have completed coursework and earned A’s through Multivariate Calculus 3 and Differential Equations, plus additional work involving stochastic partial differential equations. I can help with all aspects of Trigonometry/Pre-Calculus, including trigonometric functions and the unit circle, vector and matrix math, identifying real and complex roots (e.g. via graphs and positive real zeroes), rules of exponents and logarithms, graphing exponential and parabolic equations, identifying equations for exponential and parabolic graphs, arithmetic and geometric series, converting repeating decimals to fractions, probability (e.g. permutations, combinations, conditional and indepedent probabilities), binomial theorem and binomial trees, and real-world applications for all of these (e.g. firing cannonballs, investment portfolios, options pricing, heat diffusion). While I can mention my mathematical qualifications, students totally make my day when they write: “Wonderful Tutor!! We highly recommend Lewis!! My son was failing pre-calculus/trigonmetry before Lewis came along and his confidence was the lowest I’ve ever seen. After only 3 sessions, his grades have improved tremendously. He received a “B” on a quiz last week, and an A+ this week! Lewis provides clear explanations to a complex subject-matter through real-life examples. His passion for math is contagious!”