All of
Richard’s current tutoring subjects are listed at the left. You
can read more about
Richard’s qualifications in specific subjects below.
ACT Math
My approach to tutoring ACT Math combines (1) general strategies for approaching all math questions on the ACT, (2) domain knowledge in many areas of math, (3) test-wise tips on how to approach the ACT, and (4) practice doing ACT math problems. This approach helps students learn math in other settings as well. I have succeeded with bright students and with students who have learning issues, because I am very attentive to the each student's learning processes.
I earned a BS in mathematics at MIT, a PhD in mathematics (geometry and physics) at Berkeley, and an MBA in finance from U Chicago. I did mathematical simulation of engineering physics problems in General Electric R&D. I ran a mathematical software business for ten years where I wrote a lot of math software. I have been a leader in business analysis at several companies. I currently run a small company that sells business analysis products and services.
My experience enables me to identify and resolve the root causes behind inability to answer many kinds of math questions. For most students, the most common sources of errors on ACT Math are (1) incorrectly translating the verbal question into math concepts, (2) inability to formulate an initial strategy to approach a problem, (3) inability to apply to the ACT math they already know, and (4) not knowing the mathematics needed to solve some problems.
ACT Science
ACT Science tests skills at extracting information from data tables, graphs and text passages to justify conclusion in a scientific setting. While knowledge of related fields of science is helpful, the ACT Science test does on focus on testing knowledge of science.
I have extensive experience at interpretation of data and text. I earned a BS in math at MIT, a PhD in mathematics (geometry and physics) at Berkeley, an MBA in finance at U Chicago. I was an R&D scientist at General Electric where I got experience using data to help make engineering decisions in numerous fields. I also led business analytics projects in a number of firms, where I developed ways to use data to help make business decisions.
Algebra 1
I earned a BS in mathematics (including a lot of algebra) at MIT and a PhD in mathematics at Berkeley. I have used algebra in several small software businesses, including one mathematical software company.
Algebra 2
Algebra and geometry are the two main pillars of mathematics. Besides tutoring mathematics, I have used algebra quite extensively in several small software businesses I have run, including one mathematical software company.
My approach to teaching mathematics is to blend problem-solving with a deeper understanding of the content, and to adjust my approach to the needs of each student.
I earned a BS in mathematics at MIT and a PhD in mathematics (geometry and physics) at Berkeley.
Business
I earned an MBA in finance and marketing at U of Chicago. I have worked or consulted for 8 businesses in the Fortune 100, including General Electric headquarters and two divisions, and consulting with McKinsey & Co. McKinsey's head of industrial consulting rated me the best analyst the Firm. I have run three small software businesses, and I am currently running a small firm that provides software and services in business analytics.
Calculus
I earned a BS in mathematics at MIT and a PhD mathematics (geometry and physics) at Berkeley. As a Research Mathematician at GE R&D, I performed engineering physics simulations in numerous areas. I won a Technical Achievement Award, and published over 2 dozen internal technical reports and four papers in refereed journals.
Basic calculus contains three powerful ideas: taking limits, computing slopes of curved lines, and computing areas under curves. My approach to teaching calculus is to (a) ensure the student has a good intuitive grasp of these three basic ideas; (b) expose the student to derivations of some of the simpler formulas; and (c) help student to solve problems and to memorize the required formulas; and (d) exposing students to the tables of derivatives and integrals. I am expert in blending these approaches to fit the student’s learning style.
My main field is Riemannian geometry, which has been called "the absolute differential calculus" because it provides the most powerful approach to calculus. While teaching a student to solve problems, I try to provide richer understanding of the subject, to the extent that the student is interested.
Differential Equations
I earned a BS in math at MIT and a PhD in mathematical physics at Berkeley (NSF scholarship). I wrote a lot of symbolic, numerical and graphics software for a math software company I ran. I have solved systems of PDEs with finite element and finite difference software, including some of each kind that I wrote from scratch.
Discrete Math
I earned a BS (MIT) and PhD (Berkeley) in mathematics. At MIT I took the main undergraduate course in discrete mathematics, which focused on probability and combinatorics. For a math software company, I wrote a tutorial on how to derive the main distributions in statistical mechanics in physics from discrete combinatorics.
When teaching probability and combinatorics (which are the most common types of discrete math), I try to convey the rationale behind the formulas for permutations and combinations in various situations. The logic is quite easy, and these ideas enhance students' abilities to reason about discrete math.
Econometrics
I earned an MBA in finance at U Chicago, a BS in mathematics at MIT, and a PhD in mathematics (geometry and physics) at Berkeley. At U Chicago I took advanced electives in Bayesian statistics and quantitative finance. I have implemented a stochastic macroeconomic model of the US economy in Excel. I did outstanding analytic work in business analytics at McKinsey, where the head of industrial consulting regarded me as the best analyst in the Firm. I revolutionized business analytics at MathWorks.
I currently run ModelSheet Software, which offers software and services for business analytics.
Economics
I earned an MBA in Finance at U Chicago, and I took a minor in economics as part of my BS at MIT. I replaced many of the elementary courses in economics with advanced electives in both universities. I have practical experience applying microeconomic concepts to numerous businesses, as a consultant with McKinsey & Co. and with other companies large and small.
My approach to tutoring economics is to combine problem-solving skills with a richer understanding of the foundations.
The “neoclassical synthesis” of macroeconomics is widely viewed as outdated. It attempts to make policy prescriptions while omitting price stickiness, monopolistic competition, and including some static analysis (without time dependence). A new theory of macroeconomics that fixes these problems is emerging, under the name Dynamic Stochastic General Equilibrium models.
English
I bring an "old school" background in grammar, including outlining ideas and diagramming sentences. While students need not learn this material, it helps me to explain subtle differences in meaning among different ways of expressing an idea.
The most effective ways for students to improve English skills are to practice, to hear and read good English, and to learn formal rules. Getting explanations of subtler points from a tutor can help substantially.
English grammar is generally easier to learn than that of other major European languages, but it is less precise in some respects. Verbal skills can be improved by knowing how the characteristics of English grammar affect reading comprehension, speaking and composition. For example, English has fewer inflected endings on nouns, verbs and adjectives; instead it relies more on word order and prepositions to indicate sentence structure.
Vocabulary is an essential ingredient in good English. In my experience, a tutor can most effectively improve students' vocabulary by explaining new words as they occur in spoken or written language and in verbal tests. I can recommend vocabulary-building lists, but students can most cost-effectively do this sort of work on their own.
My strengths are in descriptive, persuasive and scientific English. I bring a mathematician's precision to analyzing the logic and smoothness of language. (My formal degrees are in mathematics, physics and finance.) I am not as experienced in writing impressionistic or fictional material.
Finance
I earned an MBA in finance from U Chicago with a minor in marketing. My studies included capital asset pricing models, valuation models for firms and investment projects, and option pricing. I have done applied financial analysis and managerial accounting projects for several clients. I have been general manager or president of several small companies where I dealt with financial analysis of the business.
I currently run a small company that markets advanced financial spreadsheet analyses.
Finite Math
I earned a BS (MIT) and PhD (Berkeley) in mathematics. At MIT I took the main undergraduate course in probability, which focused on probability and combinatorics. I have an extensive background in linear algebra. For a math software company, I wrote a software package on finite trees, and a tutorial on how to derive the main distributions in statistical mechanics in physics from discrete combinatorics.
When teaching probability and combinatorics (which are the most common types of finite math), I try to convey the rationale behind the formulas and illustrate the ideas with examples.
Geometry
More than any other part of mathematics, geometry combines intuition, computation and rigorous proof. Geometric intuition can help students to see their way through complex problems in other disciplines. I can teach geometry as problem-solving, and at a higher level to the extent that the student is receptive.
I earned a BS in math from MIT and a PhD in mathematics (geometry and physics) at Berkeley. My main field of expertise is Riemannian geometry, of which Euclidian geometry and trigonometry are the simplest cases. As a research scientist at General Electric R&D, I modeled many engineering physics problems on complicated geometrical shapes using finite element analysis.
GMAT
Besides an MBA in finance (U of Chicago), I earned a PhD in mathematics (Berkeley). I bring a mathematician's precision to logical and quantitative analysis, and to reading comprehension and grammar. I have done advanced analytics for consulting clients and as an employee at several companies.
My approach to GMAT prep is to help in four ways. First, teach test-wise tips; secondly, improve domain knowledge as needed; thirdly, refine reading and writing skills through practice and discussion; and fourth, teach specific methods for quantitative problems.
Grammar
I bring an "old school" background in grammar, including outlining ideas and diagramming sentences. While students need not learn this material, it helps me to explain subtle differences in meaning among different ways of expressing an idea.
Linear Algebra
I earned a BS in mathematics at MIT and a PhD in mathematics I ran a math software business for ten years, where I wrote plenty of symbolic and numerical software, including computation of matrix normal forms. I have written symbolic software for multilinear algebra and tensor calculus.
Logic
I earned a BS in mathematics at MIT, where I took the upper level undergraduate course in logic for math majors and got an A. I have written software that handles three-valued logic (a rather specialized topic). I also earned a PhD in mathematics (geometry and physics) at Berkeley.
Marketing
I earned an MBA from U Chicago with a minor in marketing. I have run three small software businesses where marketing reported to me. As a director of marketing and strategic planning at MathWorks, I introduced new methods of analyzing sales, marketing programs, investment projects, and customer support. I sat on the advisory boards for all 11 commercial business areas.
I have served as a product manager in a large entertainment software business, and I ran a small scientific software business where I performed or supervised all marketing activities.
I currently run a small company that markets advanced marketing analysis spreadsheets.
Mechanical Engineering
I earned a BS from MIT and a PhD in mathematical physics from Berkeley. As a research scientist at General Electric, I performed engineering physics simulations involving stress and thermal analysis of metal-glass-ceramic systems, optics, acoustics, and plasma physics; also manufacturing cost analysis. I published more than 2 dozen internal technical reports at GE and four papers in refereed journals.
Microsoft Excel
I run a small software company, ModelSheet Software, that sells advanced business analysis solutions in Excel. I have built all the models on the website. I have been doing complex analyses in spreadsheets for 20 years.
I earned a BS in math from MIT, a PhD in math from Berkeley, and an MBA in Finance from U Chicago.
Physical Science
I have broad experience in tutoring and broad experience in physical sciences.
After earning a BS from MIT and PhD in mathematical physics from Berkeley, I was a research scientist at General Electric R&D, building engineering physics simulations in many fields. At GE I delivered some seminars to staff outside their fields of expertise that were considered exceptionally understandable.
Physics
After earning a PhD in mathematical physics at Berkeley and a BS in math at MIT, I was a research scientist at General Electric R&D, where I built engineering physics simulations in many fields (stress and thermal analysis in glasses, metals and ceramics; optics; acoustics; plasma physics). I won a Technical Achievement Award, published over two dozen internal technical reports and four papers in refereed journals.
At GE R&D I delivered some seminars to staff outside their fields of expertise. These seminars were considered exceptionally understandable.
My approach to teaching physics is to develop problem-solving skills along with a strong intuitive grasp of the fundamental concepts. I strive to understand the learning processes of each student to find the right balance of approaches for that student.
Precalculus
Precalculus combines algebra with limits. Calculus has just two basic concepts: slopes of curved lines, and areas under curves. The rest is computational techniques. I am expert in tutoring these concepts and methods.
I combine teaching students to solve problems with imparting a deeper grasp of the concepts that underlie the procedures for solving problems. I also teach test-wise tips for smart test-taking. I blend these approaches to do what best fits the student’s learning style.
I earned a BS in mathematics at MIT and a PhD in mathematics (geometry and physics) at Berkeley. I also have plenty of commercial experience in engineering and business applications of calculus.
Please see my profile for more on my tutoring background.
Probability
I studied probability and statistics as part of my BS at MIT, my PhD in Mathematical Physics at Berkeley, and my MBA at U Chicago.
I have practical experience applying probability and statistics. (a) I solved an engineering quality problem at General Electric with a probability model. (b) I have written software that uses t-tests and F-tests to estimate the statistical significance of price elasticity results based on regression models. (c) I implemented a stochastic model of the US economy in Excel, based on an economics thesis from MIT. (d) I have written prototype software to do Bayesian analysis of diagnostic and therapeutic procedures in medical care and in equipment maintenance.
PSAT
I tutor PSAT, SAT and SSAT including all verbal and math material. Please see my main profile for more information on my tutoring experience.
My students on standardized tests include gifted students and students with learning issues, because I am very attentive to the students’ learning styles.
My approach to PSAT prep is to help in three ways. First, teach test-wise tips; secondly, improve domain knowledge as needed; thirdly refine reading and writing and math skills through practice and discussion.
Reading
The most important skill in good reading is to grasp the subtler distinctions between what an author is saying and something he/she is not saying. This skill requires a good understanding of grammar, followed by the ability to extract clear logical meaning from a reading passage. I bring a mathematician's precision to analyzing the logic and smoothness of language. (My formal degrees are in mathematics, physics and finance.)
For thoughtful reading materials, a strong vocabulary is also required. A tutor can most effectively improve students' vocabulary by explaining new words as they occur in spoken or written language and in verbal tests. I can recommend vocabulary-building lists, but students can most cost-effectively do this sort of work on their own.
SAT Math
I teach classes on and tutor SAT math for many students. My approach combines (1) general strategies for approaching all math questions on the SAT, (2) domain knowledge in many areas of math, (3) test-wise tips on how to approach the SAT, and (4) practice answering SAT problems. This approach helps students learn math in other settings as well. I have succeeded with bright students and with students who have learning issues, because I am very attentive to the each student's learning processes.
I earned a BS in mathematics at MIT, a PhD in mathematics (geometry and physics) at Berkeley, and an MBA in finance from U Chicago. I did mathematical simulation of engineering physics problems in general electric R&D. I ran a mathematical software business for ten years where I wrote a lot of math software. I have been a leader in business analysis at several companies. I currently run a small company that sells business analysis products and services.
My experience enables me to identify and resolve the root causes behind inability to answer many kinds of math questions. For most students, the most common sources of errors on SAT math are (1) incorrectly translating the verbal question into math concepts, (2) inability to formulate an initial strategy to approach a problem, (3) inability to apply to the SAT math they already know, and (4) not knowing the mathematics needed to solve some problems.
SAT Reading
Reading is the most complicated skill on the SAT. The SAT tests comprehension of subtle distinctions in meaning and ability to inference shades of meaning from explicit information in the text passages. I teach important test-taking tips for different types of SAT reading questions.
The most common sources of errors on SAT reading are: (1) the student gets the right general idea, but fails to comprehend the secondary distinctions for which the SAT tests; and (2) limited vocabulary can make it impossible for the student to understand some of the questions and proposed answers.
I focus on developing reading comprehension skills. There is no substitute for having an experienced tutor guide a student through the subtleties of meaning that are tested on the SAT reading test, and explaining the subtle ways that correct answers differ from incorrect answers.
Building vocabulary occurs naturally when taking SAT practice tests. I can help by explaining word roots and prefixes. Students can improve their vocabularies quite well by putting in the time to study word lists on their own or with family members.
SAT Writing
SAT Writing includes grammar, organization, paragraph and sentence structure, and writing in an interesting style.
I teach both good writing practice and how to get a high score on SAT Writing. While these two topics overlap substantially, they differ in significant ways.
The College Board’s business model is based on inexpensive automated scoring. While multiple choice testing of grammar fits this model, evaluating essays does not. This situation has major consequences for how to write a high-scoring essay for the SAT.
SSAT
I tutor SSAT, PSAT, and SAT including all verbal and math material. Please see my main profile for more information on my tutoring experience.
My students on standardized tests include gifted students and students with learning issues, because I am very attentive to the students’ learning styles.
My approach to SSAT prep is to help in four ways. First, teach test-wise tips; secondly, improve domain knowledge as needed; thirdly, refine reading and writing skills through practice and discussion; and fourth, teach specific methods for quantitative problems. We also write essays.
Trigonometry
Trigonometry can seem daunting because of the complexity of the formulas. The solution to this challenge is to develop a deeper geometric understanding of what is going on.
My approach to teaching mathematics is to blend problem-solving with a deeper understanding of the content. Unlike most tutors, I know how to teach mathematics as a science, not just as a way to solve problems. Please see my overall profile for information about my tutoring qualifications.
I earned a BS in math from MIT and a PhD in math from Berkeley. My main field of expertise is Riemannian geometry, of which Euclidian geometry and trigonometry are the simplest cases.
Vocabulary
Vocabulary is an essential ingredient in good English. In my experience, vocabulary is the most important factor limiting verbal scores on SAT reading. A tutor can most effectively improve students' vocabulary by explaining new words as they occur in spoken or written language and in verbal tests. I can recommend vocabulary-building lists, but students can most cost-effectively do this sort of work on their own.