MIT PhD for Tutoring in Math, Physics, and Other Fields

William L.
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MIT PhD for Tutoring in Math, Physics, and Other Fields

William L.
I am available to tutor any area of mathematics: arithmetic, algebra, geometry, trigonometry, calculus, statistics, linear algebra, differential equations, etc. I can also help with more advanced college-level topics. My experience with advanced mathematics gives me insight into how different mathematical concepts are connected, which means that I can present these ideas in several different ways. So if one way of looking at a problem doesn't work for you, I can find others! I remember my...

Mathematics, physics

PhD

Graduate Coursework

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GMAT,
GRE

Latin,
#### Latin

I studied Latin in middle school and high school. I earned a perfect score on the ACL/NJCL National Latin Exam four times.

Statistics,
#### Statistics

I studied probability and statistics in college as part of a math major. Some of the topics I can help with include combinatorics and counting arguments, calculating statistical properties of a sample, and random variables and probability distributions.

GMAT
Elementary Math

Algebra 1,
#### Algebra 1

Algebra, geometry, and trigonometry are fundamental to more advanced topics in math, so I use them every day. I can explain the concepts and how to use them to solve problems.

Algebra 2,
#### Algebra 2

Algebra 2 is fundamental to so much of mathematics. I've used it in every math class I've taken and in my own independent work. But I remember when I was learning the topic myself, and so I know some ways of making the topic make sense by relating it to other areas of math and to real-world situations.

Calculus,
#### Calculus

As the study of varying quantities, calculus is essential to much of advanced mathematics as well as other scientific and quantitative areas. The main ideas are the derivative, the integral, and how they relate to each other. I am experienced tutoring high school and college calculus, AP Calculus AB and BC, multivariable calculus, as well as more advanced calculus-related classes such as real analysis.

Physics,
#### Physics

In college, I took classes in mechanics, electricity and magnetism, thermodynamics, and quantum mechanics as part of a physics major. I can help make sense of any of those topics.

Precalculus,
#### Precalculus

Precalculus can include a range of topics from fields such as algebra, geometry, and trigonometry, as well as some introductory calculus concepts like limits. I excelled in all of these classes in school, and I use them all the time in higher-level math work. I can help you understand any of these precalculus concepts and use them successfully to solve problems!

Statistics,
#### Statistics

I studied probability and statistics in college as part of a math major. Some of the topics I can help with include combinatorics and counting arguments, calculating statistical properties of a sample, and random variables and probability distributions.

Geometry,
Prealgebra,
SAT Math
Latin
#### Latin

I studied Latin in middle school and high school. I earned a perfect score on the ACL/NJCL National Latin Exam four times.

Algebra 1,
#### Algebra 1

Algebra, geometry, and trigonometry are fundamental to more advanced topics in math, so I use them every day. I can explain the concepts and how to use them to solve problems.

Algebra 2,
#### Algebra 2

Algebra 2 is fundamental to so much of mathematics. I've used it in every math class I've taken and in my own independent work. But I remember when I was learning the topic myself, and so I know some ways of making the topic make sense by relating it to other areas of math and to real-world situations.

Calculus,
#### Calculus

As the study of varying quantities, calculus is essential to much of advanced mathematics as well as other scientific and quantitative areas. The main ideas are the derivative, the integral, and how they relate to each other. I am experienced tutoring high school and college calculus, AP Calculus AB and BC, multivariable calculus, as well as more advanced calculus-related classes such as real analysis.

Differential Equations,
#### Differential Equations

I've taken courses in differential equations from both abstract and concrete points of view. Because of this, I can explain both methods of solving particular differential equations and theorems about the existence, uniqueness, and behavior of equations of certain types. I have experience teaching the subject, having worked as a teaching assistant for the introduction to differential equations course at MIT.

Discrete Math,
#### Discrete Math

Discrete math is a wide subcategory of mathematics which can include logic, set theory, combinatorics, graph theory, game theory, and other topics. I took several courses in these areas in high school and college and excelled in them. I can help students understand the concepts and construct mathematical proofs in these areas.

Finite Math,
#### Finite Math

Finite math includes a range of topics that vary from course to course but may include matrix algebra; introductory combinatorics, probability, and statistics; linear programming; and symbolic logic. I have taken courses in all of these topics in the process of earning a degree in math, and I have taught them to students from middle school through college.

Linear Algebra,
#### Linear Algebra

Matrices and linear transformations, the principal concepts of linear algebra, are essential to many areas of mathematics. I have studied them in courses including multivariable calculus (the idea of linear functions is essential to this topic), abstract algebra (where you learn that matrices can be put into certain standard forms), and functional analysis (a generalization of linear algebra to "infinite matrices"). In addition to explaining how to do calculations in linear algebra, I can also help you with the underlying mathematical theory when that would be useful for your purposes. I hold a bachelor's degree from UChicago and a doctorate from MIT, both in mathematics.

Physics,
#### Physics

In college, I took classes in mechanics, electricity and magnetism, thermodynamics, and quantum mechanics as part of a physics major. I can help make sense of any of those topics.

Precalculus,
#### Precalculus

Precalculus can include a range of topics from fields such as algebra, geometry, and trigonometry, as well as some introductory calculus concepts like limits. I excelled in all of these classes in school, and I use them all the time in higher-level math work. I can help you understand any of these precalculus concepts and use them successfully to solve problems!

Probability,
#### Probability

I studied probability and statistics in college as part of a math major. Some of the topics I can help with include combinatorics and counting arguments, calculating statistical properties of a sample, and random variables and probability distributions.

Statistics,
#### Statistics

I studied probability and statistics in college as part of a math major. Some of the topics I can help with include combinatorics and counting arguments, calculating statistical properties of a sample, and random variables and probability distributions.

Trigonometry,
#### Trigonometry

I use trigonometry all the time because it's fundamental for understanding shapes and because it ties in to all areas of math. I have taught it as part of various classes such as algebra, calculus, and geometry.

Geometry,
Prealgebra,
SAT Math
Algebra 1,
#### Algebra 1

Algebra, geometry, and trigonometry are fundamental to more advanced topics in math, so I use them every day. I can explain the concepts and how to use them to solve problems.

Algebra 2,
#### Algebra 2

Algebra 2 is fundamental to so much of mathematics. I've used it in every math class I've taken and in my own independent work. But I remember when I was learning the topic myself, and so I know some ways of making the topic make sense by relating it to other areas of math and to real-world situations.

Calculus,
#### Calculus

As the study of varying quantities, calculus is essential to much of advanced mathematics as well as other scientific and quantitative areas. The main ideas are the derivative, the integral, and how they relate to each other. I am experienced tutoring high school and college calculus, AP Calculus AB and BC, multivariable calculus, as well as more advanced calculus-related classes such as real analysis.

Physics,
#### Physics

In college, I took classes in mechanics, electricity and magnetism, thermodynamics, and quantum mechanics as part of a physics major. I can help make sense of any of those topics.

Precalculus,
#### Precalculus

Precalculus can include a range of topics from fields such as algebra, geometry, and trigonometry, as well as some introductory calculus concepts like limits. I excelled in all of these classes in school, and I use them all the time in higher-level math work. I can help you understand any of these precalculus concepts and use them successfully to solve problems!

Physics
#### Physics

In college, I took classes in mechanics, electricity and magnetism, thermodynamics, and quantum mechanics as part of a physics major. I can help make sense of any of those topics.

Chess
#### Chess

I'm a tournament chess player who has an Expert-level rating from the US Chess Federation. I've played thousands of tournament games. I'm available to analyze games with students and for help with specific techniques.

ASVAB,
GED,
GMAT,
GRE,
SAT Math

William has provided examples of their subject expertise by answering **1 question** submitted by students on Wyzant’s Ask an Expert.

## Excellent tutor

William knows a lot about Partial Differential Equations and can explain the thought process in very clear steps and words. He also can help identify gaps in knowledge that will be necessary for later on so that they can be patched up earlier instead of later. Thank you very much, William!

Benjamin, 2 lessons with William

## Knowledgeable and Friendly Tutor

He knows graduate level functional analysis which is a hard skill to find. He knows his material and is very friendly in helping. I'm glad I got his help. Thank you so much!

Kurt, 1 lesson with William

## Physics

William was very patient and knowledgeable. He did excellent job with my daughter. I know that after only one session that it can be hard to do an evaluation but if it continues like last session, I have no doubt that it will definitely help my daughters confidence, after all she hates any kind of math. Thank you William

Kerry, 29 lessons with William

## William is an excellent tutor. He is smart, patient, and he really explains fundamentals. Sometimes we are stuck because we are missing foundation. Willian knows how to fill in the gaps.

Willian taught some concepts for my linear algebra and discrete math course. There were some elements that were confusing to me, and he was able to clarify a lot. He is a very well-versed tutor, so breaking down the elements I needed assistance with seemed easy for him. I was able to complete my homework assignment on my own after his instruction.

Jessica, 1 lesson with William

## Helpful tutor

William took his time to made I understand the question, also he provided background to the question that ill be able to understand better. Overall he was great.

Sherlin, 1 lesson with William

## Highly recommend! Fantastic tutor!

William was an absolutely fantastic tutor. I met with William several times to prepare for my final exam in an advanced college linear algebra class. William is incredibly knowledgeable and his clear, concise explanations were exactly what I needed. It was especially impressive because I never had to send messages ahead of time giving him specific concepts or problems I wanted to review. No matter what topic I brought up, William had the answers. Highly recommend A+++.

Judy, 6 lessons with William

## Knowledgeable and patient tutor

William was very patient, helpful, knowledgeable on diff equation subject and problems. Also, responded promptly and tutored with limited advance notice. He is also very technology savvy - also appreciated! Absolutely planning to set up more regular tutor schedule! Thank you!

Ginger, 64 lessons with William

## Knowledgeable and Helpful with Linear Algebra

He allowed me to learn at my pace and taught accordingly. He was very clear with explanations and ensured that every step towards the solution had a purpose and was correct. I enjoyed my first session a lot!

Nathan, 1 lesson with William

## Patient and Supportive Tutor!

I started taking a discrete math class that previous students said was very hard. Once I started the class, I knew I needed help. It is very hard to find a math tutor who is good at explaining discrete math concepts because the class is a smorgasbord of loosely related math subjects. Thankfully I found William. He is great at taking abstract concepts and breaking them down into easier step-by-step processes. As well, he is very patient and supportive. If you’re taking discrete math, I can’t recommend William enough!

Todd, 30 lessons with William

## Great Tutor

William is a fantastic tutor, who explained some tough concepts in terms I could understand. He also worked with me through some tricky problems, and showed me a few new tools for evaluating multivariable limits.

Darcy, 12 lessons with William