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Friendly and Patient PhD Math Tutor
James M.

5.0 (1,465 ratings)

6,219 hours tutoring

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About James

Bio

James is a full time tutor with a strong background in computational science and mathematics. He holds a B.S. in Chemistry with a minor in Control and Dynamical Systems from Caltech and earned his Ph.D. in Computational Science, Engineering, and Mathematics from UT Austin, supported by the prestigious DOE CSGF fellowship.

James tutors a broad range of mathematics subjects, from high school to graduate-level coursework, including all levels of calculus, differential equations, PDEs, linear...

James is a full time tutor with a strong background in computational science and mathematics. He holds a B.S. in Chemistry with a minor in Control and Dynamical Systems from Caltech and earned his Ph.D. in Computational Science, Engineering, and Mathematics from UT Austin, supported by the prestigious DOE CSGF fellowship.

James tutors a broad range of mathematics subjects, from high school to graduate-level coursework, including all levels of calculus, differential equations, PDEs, linear algebra, real and complex analysis, probability, and many special topics. He has extensive experience helping students master difficult concepts, develop problem-solving skills, and build confidence in their abilities. He has also guided many students through AP Calculus preparation and occasionally assists with standardized test prep.

With a personalized approach tailored to each student's needs, James excels at making abstract concepts clear and applicable. Whether you're looking for support with coursework, exam preparation, or a deeper understanding of mathematics, James is dedicated to helping you achieve your academic goals.

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Education

California Institute of Technology
Chemistry
University of Texas at Austin
PhD

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Approved Subjects

Calculus

Calculus

I completed multivariable calculus in high school and earned a 5 on the AP Calculus BC exam. At Caltech and UT Austin, nearly all of my coursework built upon this foundation, deepening my understanding of calculus and its applications in science and engineering. Even now, I use calculus regularly in my daily life. Teaching calculus is one of my favorite things because it transforms the way students see mathematics. I regularly help students with all levels of calculus, from AP Calculus to college Calculus 1 and 2, as well as multivariable calculus. Whether you're encountering calculus for the first time, looking to refine your understanding, or studying advanced topics, I can help you develop a strong conceptual foundation, master problem-solving techniques, and appreciate the power of calculus in real-world applications.
Differential Equations

Differential Equations

Over seven years of dedicated tutoring, I have helped many students demystify differential equations, overcome academic hurdles, and achieve their goals. A unique challenge of this subject is that it requires students to synthesize calculus, algebra, and physics simultaneously. My instruction explicitly bridges the gap between the computational side—mastering analytical techniques like Laplace transforms and series solutions—and the geometric side, using phase portraits and direction fields to build a strong physical intuition for how systems evolve. I love teaching differential equations because they are the mathematical language of change, serving as the essential gateway to modeling everything from quantum mechanics and biological populations to financial markets. Ultimately, whether your goal is to master the analytical mechanics of the subject or build a deeper intuition for physical modeling, I can help you unlock your full mathematical potential.
Discrete Math

Discrete Math

I earned my PhD in Computational Science from UT Austin, specializing in Applied Mathematics and Computer Science. In my PhD research I utilized fundamental discrete math principles, including probability and algorithm complexity analysis to understand complex real-world problems. I have tutored full-time for seven years and have broad experience in logic, set theory, graph theory, proof techniques, and combinatorics. I help students succeed by breaking down difficult mathematical concepts into their fundamental components. This enables students to understand challenging material, and utilize it to solve problems!
Linear Algebra

Linear Algebra

Over seven years of dedicated tutoring, I have helped many students demystify linear algebra, overcome academic hurdles, and achieve their goals. A unique challenge of the subject is that it demands mastery over two distinct domains: the computational (matrix operations, algorithms, and applications) and the abstract (vector spaces, proofs, and structural thinking). My instruction explicitly bridges this gap, ensuring students can build a rigorous theoretical intuition while gaining hands-on mastery over computational tools like MATLAB, Octave, or key Python numerical libraries such as NumPy. I am genuinely passionate about teaching linear algebra because it serves as the essential gateway to so many advanced fields, from differential equations to machine learning, and also provides the foundation for almost any form of computational mathematics. My goal is to move beyond rote memorization, providing the clarity, patience, and tailored guidance you need to conquer both the calculations and the proofs, ultimately unlocking your full mathematical potential.
MATLAB

MATLAB

I have over 20 years of experience working with computational tools such as MATLAB, Octave, and key numerical libraries in Python such as NumPy. I developed a MATLAB library as part of my PhD thesis for sampling high dimensional distributions stemming from Bayesian statistical inverse problems. I still use Octave (the freeware version of MATLAB) today with my current students, and for my own personal use with recreational mathematics.
Algebra 1
Algebra 2
Geometry
Prealgebra
Precalculus
Probability
Statistics
Trigonometry
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Ratings and Reviews

Rating

5.0 (1,465 ratings)
5 star
(1,452)
4 star
(12)
3 star
(1)
2 star
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1 star
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Reviews

EXTREMELY HELPFUL TUTOR!!

I was very anxious about my final exam in Linear Algebra, as I had fallen behind the entire semester and struggled to grasp the concepts. James came to my rescue, and we had an incredibly productive and diligent session. His skillful teaching was evident! I left our session a transformed student, and after taking the exam, I felt confident in my performance because of him! If you ever need help with your studies, James is definitely the tutor to seek out—even if you're a whole semester behind with just one night to catch up. He has an exceptional command of math and patiently broke down the concepts for me, even when I asked him to explain how to solve a problem five times haha. Each time he explained it in a new way that helped me comprehend. It's safe to say that he is truly an outstanding tutor.

Victoria, 1 lesson with James

Patient and excellent teacher!

My son is taking Algebra 2 Honors and needed some help with an assignment. James was so patient and answered all of his questions. My son said he felt more confident after the session. I would highly recommend James! We will definitely continue using his tutoring services!

Mandy, 1 lesson with James

Outstanding!

James was an excellent tutor for University Calc II. Son went from failing to a B in 5 weeks. His confidence improved so much he’s considering calc III. James was very easy to work with and always was quick to respond. He made a huge difference in my son’s college experience. Recommend 5 stars all the way. Worth every penny

Jon, 9 lessons with James

Literal Life saver

I had explained to James that my extremely smart senior was behind on her college math course, and the stress of it was really too much. He said, no worries, I can help. He more than helped. After her first session she said, I forgot that I love math and I’m good at it. Don’t hesitate, hire him.

Brittany, 17 lessons with James

Knowledgeable and accommodating when you are in a time

James tutored my son . He was having trouble understanding some concepts for Calc 1 for his mid terms James did a great job tutoring him . He clarified many concepts and made sure he was well prepared for the tests. He is a great tutor and would highly recommend him!

Shamini, 3 lessons with James

A wonerful help w/multivariable calculus

My son appreciates the way James is able to explain complex problems with great clarity and offers multiple layers of rationale. He finds James efficient, making very good use of their time together. James is friendly and earnest and eager to help, and my son sincerely enjoys meetings with him.

Andrea, 17 lessons with James

Good explanations of troublesome problems

My student felt shaky before a test and asked to meet with a tutor. James M. was a great choice - he patiently walked through sample problems, explaining the steps along the way. Over the course of the next few days before the test, my student practiced many more hours, using the concepts reviewed with James. The night before the test, my student once again felt confident in math. We will definitely contact James again if another review is needed!

BT, 1 lesson with James

Phenomenal

Incredible tutor and “wicked smart” as my son said. Extremely knowledgeable and great at explaining concepts. Truly helped my son learn and understand his differential equations class and we couldn’t be more appreciative.

V, 5 lessons with James

Great tutor for any skill level

Prior to taking differential equations, I had not taken a core math class in approximately 2 years. James was able to help me better understand the fundamental concepts I was learning despite having lost some knowledge in between my extended gap in classes. James was always available when I needed, he responded quickly and, I felt like he always had a thorough understanding of any topic I asked. On top of this, he was able to help guide me to the answer rather than just giving it to me outright which helped me better understand the material. I highly recommend this tutor for people of any mathematical skill level.

Chance, 19 lessons with James

“Legend” is how my son described James!

My son felt hopeful and encouraged after his first session with James. He will continue to lean on James to help him through his calculus I & II and linear algebra courses at university. He especially liked how collaborative the session felt and how knowledgeable James is with the material! We found the right tutor for our son. What a blessing!

Lilly, 2 lessons with James