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Award-Winning Convex geometry Tutors

Mimi

Certified Tutor

6+ years

Mimi

Masters in Education, Education
Mimi's other Tutor Subjects
Middle School Math
Calculus
Algebra
Elementary School Math

I am an interdisciplinary educator with an Ed.M. from the Harvard Graduate School of Education and a B.A. from Dartmouth College. My background is primarily in integrated arts learning and museum education and I specialize in visual arts, history and art history, and object-based learning. In all su...

Education

Harvard University

Masters in Education, Education

Dartmouth College

B.A.

Test Scores
SAT
1560
Aaron

Certified Tutor

10+ years

Aaron

Current Grad Student, Mechanical Engineering
Aaron's other Tutor Subjects
Pre-Algebra
Calculus 2
Calculus
Algebra

I'm not tutoring or buried in my textbooks, you will either find me rock climbing at the Triangle Rock Club, playing Ultimate Frisbee, working on my car, or enjoying the great outdoors (beaches, mountains, forests--you name it, I love it). On rainy weekends I enjoy tinkering with computers and old e...

Education

The University of Texas at Dallas

Bachelors, Mechanical Engineering

Duke University

Current Grad Student, Mechanical Engineering

Test Scores
SAT
1530

Certified Tutor

10+ years

Nina

Masters in biostatistics
Nina's other Tutor Subjects
Statistics Graduate Level
Statistics
Calculus
Algebra

I am a recent graduate from a masters program in biostatistics at Columbia University. I received my Bachelor of Arts in biological sciences, with a focus in neurobiology at Northwestern University. In August, I will be starting a doctoral program in biostatistics at NYU. I was a teaching assistant ...

Education

Columbia University

Masters in biostatistics

Northwestern University

Bachelor of Arts in biological sciences (focus in neurobiology)

Columbia University in the City of New York

Current Grad Student, Biostatistics

Test Scores
SAT
1550

Certified Tutor

Reid

PHD, Education
Reid's other Tutor Subjects
Pre-Algebra
Middle School Math
Calculus
Algebra

I am a graduate of Wesleyan University, where I received my Bachelor of Arts in Sociology with High Honors. With eight years of experience working in education, I've tutored students in math, science, history, and English, as well as helped students prepare for standardized tests. I've guided adults...

Education

Harvard University

PHD, Education

Wesleyan University

Bachelor in Arts, Sociology

Test Scores
ACT
32

Certified Tutor

8+ years

Solange

Bachelor in Arts (Sociology & Women's Studies)
Solange's other Tutor Subjects
Calculus
Algebra
ACT Writing
Public Speaking

I'm Solange - a recent graduate from Harvard where I studied Sociology & Women's Studies. I've been tutoring for eight years now, and have worked with a wide range of ages and in a wide range of subjects. Some of my specialties are college prep/test taking II worked in the admissions office on campu...

Education

Harvard University

Bachelor in Arts (Sociology & Women's Studies)

Test Scores
ACT
34

Certified Tutor

Charles

Bachelor of Science, Mechanical Engineering
Charles's other Tutor Subjects
AP Calculus AB
Pre-Algebra
Algebra 3/4
Trigonometry

I am a junior Mechanical Engineering major at Yale, and I hope to become a Naval Aviator after college. I am also a varsity sailor, and enjoy playing music with friends when I can get some free time. I have been tutoring my fellow students throughout my entire academic career, and I would best descr...

Education

Yale University

Bachelor of Science, Mechanical Engineering

Test Scores
SAT
1440
ACT
34

Certified Tutor

Michelle

Current Grad Student, M.D.
Michelle's other Tutor Subjects
Pre-Algebra
Pre-Calculus
Geometry
Calculus

I am proud to be a part of Varsity Tutors! I am originally from San Antonio, TX; I completed my undergraduate education at Rice University in Houston where I received a bachelor's degree in Biochemistry and Cell Biology. Currently, I am in my second year of medical school at Baylor College of Medici...

Education

Baylor College of Medicine

Current Grad Student, M.D.

Rice University

Bachelor's in Biochemistry and Cell Biology

Test Scores
SAT
1570

Certified Tutor

Christopher

Bachelor of Science, Mechanical Engineering
Christopher's other Tutor Subjects
AP Calculus AB
College Algebra
Algebra 3/4
Trigonometry

I am a rising sophomore at Harvard College and am about to declare as a Mechanical Engineering concentrator, working towards a Bachelor of Science degree. I've always enjoyed sharing my knowledge with my peers and those around me and have done so in both formal and informal settings. I've been a tut...

Education

Harvard College

Bachelor of Science, Mechanical Engineering

Test Scores
ACT
35

Certified Tutor

Liz

Masters, Special Education: Mild to Moderate Disabilities 5-12
Liz's other Tutor Subjects
Pre-Algebra
Middle School Math
Calculus
Algebra

I am a graduate of Washington University in St Louis, where I received my Bachelor of Arts in History with minors in Humanities and Anthropology. Since graduation, I have worked as a tutor, teacher, and director of tutors at a charter public middle school in Boston. During this time I also received ...

Education

Simmons College

Masters, Special Education: Mild to Moderate Disabilities 5-12

Washington University in St. Louis

Bachelor of Arts in History (minors in Humanities and Anthropology)

Test Scores
ACT
34

Certified Tutor

9+ years

Justin

Doctor of Philosophy, Computational Mathematics
Justin's other Tutor Subjects
AP Calculus BC
AP Calculus AB
Pre-Algebra
Multivariable Calculus

I am an aspiring applied mathematician, with particular interest in image processing and climate science. I graduated in May 2017 from Washington University in St. Louis with a bachelor's in physics and mathematics, and am beginning a PhD program in September 2017 at the University of Chicago in Com...

Education

Washington University in St. Louis

Bachelor's in Physics and Mathematics

University of Chicago

Doctor of Philosophy, Computational Mathematics

Test Scores
SAT
1560
ACT
33

Certified Tutor

9+ years

Henry

Bachelor in Arts, History
Henry's other Tutor Subjects
Calculus
Algebra
AP Environmental Science
PSAT Writing Skills

I'm eager to help you in your education. I'm a recent graduate of Harvard College looking to apply to law school. My senior thesis was written on John Dewey's ideas of education, which I deeply believe has incredible power to transform individuals and society.

Education

Harvard College

Bachelor in Arts, History

Test Scores
SAT
1530

Certified Tutor

James

Bachelor in Arts, Chemistry
James's other Tutor Subjects
AP Calculus AB
Algebra 3/4
Geometry
Calculus

I am currently a senior at Harvard College where I study chemistry, and I'll be attending Columbia Medical School next year. I have years of experience tutoring college students in math (mostly calculus) and chemistry including both general and organic chemistry. In addition, I am very familiar with...

Education

Harvard University

Bachelor in Arts, Chemistry

Test Scores
SAT
1570

Certified Tutor

6+ years

Ingrid

Bachelor of Science, Biomedical Engineering
Ingrid's other Tutor Subjects
Pre-Algebra
Finite Mathematics
Trigonometry
Statistics

I am exploring my creativity by pursuing a double major in Asian Languages and Cultures with a focus in Korean, studying abroad in South Korea as a Benjamin A. Gilman Scholar, leading workshops that teach 3D printing and CAD for undergraduate students as the president of 3D4E, advocating for the fir...

Education

Northwestern University

Bachelor of Science, Biomedical Engineering

Test Scores
SAT
1540
ACT
33

Certified Tutor

9+ years

Isabella

Current Grad Student, Operations Research
Isabella's other Tutor Subjects
Pre-Algebra
Middle School Math
Geometry
Calculus

I am a graduate of MIT. I received my Bachelor of Science in Mathematics with minors in Management Science and Ancient and Medieval Studies. Since graduation, I have started my PhD at Georgia Tech in Operations Research. Throughout my career I have TA'd several math and computer science courses at t...

Education

Massachusetts Institute of Technology

Bachelor of Science in Mathematics (minors in Management Science and Ancient and Medieval Studies)

Georgia Institute of Technology-Main Campus

Current Grad Student, Operations Research

Test Scores
SAT
1510

Certified Tutor

10+ years

Daniel

Bachelors
Daniel's other Tutor Subjects
Pre-Algebra
Middle School Math
Calculus
Algebra

I am excited to be home and help fellow straphangers on their educational paths! My largest wealth of tutoring experience is in foreign languages--particularly French--but I also feel very comfortable editing essays of any kind and working through standardized test concepts. My availability is extre...

Education

Brown University

Bachelors

Test Scores
SAT
1500

Meet Varsity Tutors Experts

Connect with highly-rated educators ready to help you succeed.

Henry

Calculus Tutor • +41 Subjects

I'm eager to help you in your education. I'm a recent graduate of Harvard College looking to apply to law school. My senior thesis was written on John Dewey's ideas of education, which I deeply believe has incredible power to transform individuals and society.

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James

AP Calculus AB Tutor • +40 Subjects

I am currently a senior at Harvard College where I study chemistry, and I'll be attending Columbia Medical School next year. I have years of experience tutoring college students in math (mostly calculus) and chemistry including both general and organic chemistry. In addition, I am very familiar with all sections of the SAT and ACT having prepared several high school students for these tests. I believe that every student is capable of boosting his or her baseline score on these tests, so long as he or she works hard to get to know the format of the tests and the most popular types of questions. I tutor because I love seeing students develop a genuine passion for the subjects they once disliked (such as math and science), once they understand the power of these subjects and their applications to the real world.

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Ingrid

Pre-Algebra Tutor • +51 Subjects

I am exploring my creativity by pursuing a double major in Asian Languages and Cultures with a focus in Korean, studying abroad in South Korea as a Benjamin A. Gilman Scholar, leading workshops that teach 3D printing and CAD for undergraduate students as the president of 3D4E, advocating for the first-generation and low-income student community as the Outreach Chair of the Quest+ Scholars Network, and getting involved with the Society of Women Engineers' outreach committee. I currently hold a work-study position as an administrative clerical aide in the Institute of Sustainability and Energy at Northwestern and was an undergraduate researcher in the John Rogers Lab. As I look forward with aspirations of applying to graduate school, areas of research in biomedical engineering and biotechnology that I am particularly interested in include biomaterials, pharmaceuticals, and drug delivery systems. Outside of the classroom, I enjoy learning on my own and sharing my experience and knowledge with my peers and other students. I hope to make use of my experiences with academics and learning in high school and so far in my undergraduate career in order to effectively tutor students who may be experiencing the same struggles in learning that I also experienced.

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Isabella

Pre-Algebra Tutor • +27 Subjects

I am a graduate of MIT. I received my Bachelor of Science in Mathematics with minors in Management Science and Ancient and Medieval Studies. Since graduation, I have started my PhD at Georgia Tech in Operations Research. Throughout my career I have TA'd several math and computer science courses at the college level. I have also taught at summer programs for gifted middle school and high school students. I am passionate about tutoring kids in math and science because I think that a strong foundation in STEM at an early age can set the tone for their future. In my spare time I like to engage in athletics, and was a Division 1 rower in college. Hobbies: reading, swimming, writing, books, music, running, art

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Daniel

Pre-Algebra Tutor • +26 Subjects

I am excited to be home and help fellow straphangers on their educational paths! My largest wealth of tutoring experience is in foreign languages--particularly French--but I also feel very comfortable editing essays of any kind and working through standardized test concepts. My availability is extremely flexible, and anywhere in New York City works for me. I look forward to working with you.

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Elena

Calculus Tutor • +31 Subjects

I am a graduate of McGill University (BA First Class Honors) and the University of Edinburgh (MSc First Class Honors with Distinction) with over eight years of tutoring experience. I am currently a curriculum developer for a company which creates relatable and culturally-literate courses for middle and high-schools, and am particularly adept at communicating and explaining concepts in a quirky, engaging, and intelligent manner. I was named Scotland International Young Thinker of the Year 2014 for exactly that sort of work. Much of my tutoring background is in test-prep and essay coaching, which I enjoy because it allows the tutor and student to think strategically together, and work as a team to achieve concrete results. I have worked with students ranging in age from 6-32, and believe that, in an educational context, a few jokes never hurt anybody. I love reading and learning, and my educational approach is centered around making the material just as engaging to students as it is to me. I think J.K. Rowlings, the writer of Harry Potter, is just as brilliant as Stephen Hawking, and in my free time, I manage my (terrible) fantasy baseball team, write songs for my comedy band, and crack jokes about terrible science-fiction movies with my friends.

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Justin

Calculus Tutor • +38 Subjects

I am a graduate of the University of Chicago where I received my Bachelor of Arts in Philosophy. Currently, I am in the master's program at the University of New Mexico where I am continuing my education in philosophy. Ultimately, I hope to go on to earn a PhD in Philosophy so that I can continue engaging in my passions for learning and teaching. While in school, I have spent countless hours coaching high school speech and debate both in person and working online with students across the country. My focus in coaching has been to emphasize philosophy and critical thought to prepare students to think through novel arguments on their own. I am passionate about teaching and tutoring because I love seeing students learn to be intellectually independent and think through problems on their own terms by developing their critical thinking skills. I have devoted my life to education because I am passionate about it, and I try to share some of my passion for learning with the students I work with. I tutor all sorts of Standardized Tests, and I particularly enjoy working on logic-based problems like analogies and math sections. When I am not tutoring or reading for school, I enjoy strategy games (both board games and video games), listening to music, hiking, playing basketball, and just relaxing with friends.

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Asta

Pre-Algebra Tutor • +73 Subjects

I am a graduate of the University of Chicago where I received my undergraduate degree in political science. Right after graduation, I worked as an academic and test prep tutor as well as admissions consultant in Hong Kong. For the past two years, I worked with a number of students to help prepare them for college in the United States.

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Sabira

Middle School Math Tutor • +35 Subjects

I am currently attending Johns Hopkins University, pursuing a dual degree in Computer Science and Applied Math and Statistics. I love helping students and I love the feeling I get knowing that I was able to use my knowledge to make someone else happier. My favorite subject to teach is math because there are so many ways to learn it and if one way does not help I can use another. I used to teach taekwondo and interacted with all kinds of students, and I'm excited to help out more! Hobbies: books, reading, music, writing, art

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Andrew

Pre-Algebra Tutor • +26 Subjects

I am comfortable tutoring math subjects up to multivariable calculus and differential equations, as well as college physics. Hobbies: books, music, art, reading, writing

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Frequently Asked Questions

Students typically struggle most with visualizing higher-dimensional convex sets and translating between algebraic and geometric representations. Common pain points include understanding the relationship between vertices, edges, and faces in polytopes, working with convex hulls and their properties, and proving convexity using linear combinations and half-space intersections. Many students also find it difficult to grasp why certain optimization problems are easier to solve when constraints form convex regions, and how to recognize when a feasible region is convex versus non-convex.

A tutor can break down convex geometry proofs by first establishing the foundational definitions—like showing why a set is convex if every line segment between two points stays within the set. They help you recognize proof patterns, such as using linear combinations to verify convexity or applying the separating hyperplane theorem strategically. Tutors also teach you to sketch examples in 2D or 3D before tackling abstract n-dimensional cases, which builds intuition for why certain theorems hold and makes the logical steps feel less arbitrary.

Visualization is critical in convex geometry because geometric intuition often reveals why theorems are true and how to apply them correctly. Many students can memorize definitions but struggle to picture what a convex polytope or a cone actually looks like in higher dimensions. Tutors help by starting with concrete 2D and 3D examples, using sketches and diagrams to show how vertices connect, how constraints create feasible regions, and how the geometry changes as you modify parameters. This visual foundation makes abstract proofs and optimization problems much more accessible.

This connection is one of the biggest conceptual leaps in convex geometry—moving between inequalities like Ax ≤ b and the actual geometric shape they define. A tutor can help you see that each linear inequality represents a half-space, and their intersection forms a convex polytope. They teach you to recognize patterns: a system of inequalities that has a solution means the feasible region is non-empty, and the vertices of that region are where constraints become active. By working through examples where you write inequalities from a sketch and then verify the geometry algebraically, you develop fluency in both directions.

Convex geometry is fundamental to optimization because convex problems have unique global minima and can be solved efficiently, while non-convex problems may have multiple local minima. A tutor helps you understand why a linear objective function over a convex polytope is optimized at a vertex, and how to recognize when a constraint set is convex (making the problem tractable). They also show you how to verify convexity of objective functions using second derivatives or the definition, and why this matters for choosing the right algorithm. This connection transforms convex geometry from abstract theory into a practical tool for solving real-world problems.

Moving beyond 3D is challenging because you can't draw it, but a tutor teaches you to reason algebraically while grounding concepts in lower dimensions. For example, understanding that a hyperplane in n dimensions is defined by a single linear equation (just like a plane in 3D or a line in 2D) helps you generalize the concept. Tutors also help you use analogies—a 4D hypercube relates to a 3D cube the way a cube relates to a square—and practice working with explicit examples in 4D or 5D using coordinates. By consistently translating between dimension-specific intuition and general algebraic definitions, you develop the mental flexibility to work confidently in any dimension.

In convex geometry, showing work means clearly stating which definitions or theorems you're using, not just the final answer. For example, when verifying that a set is convex, write out the definition (for any two points in the set, their convex combination is also in the set), then explicitly show the algebraic steps. When solving optimization problems, state your constraints, explain why the feasible region is convex, identify the vertices, and show how you evaluated the objective function at each one. A tutor can help you develop this habit by reviewing your solutions and pointing out where your reasoning jumps are, so you build a clear, logical presentation that demonstrates genuine understanding.

An effective convex geometry tutor should have strong foundational knowledge in linear algebra, multivariable calculus, and real analysis, since these underpin the subject. They need hands-on experience with convex optimization, polytopes, and geometric reasoning—ideally from coursework, research, or applied work in operations research, machine learning, or mathematics. Beyond subject expertise, they should be able to explain abstract concepts clearly, sketch diagrams effectively, and recognize where students are getting stuck conceptually versus procedurally. Varsity Tutors connects you with tutors who combine deep subject knowledge with the ability to build your geometric intuition from the ground up.

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