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Jane
I am a current student at Princeton University, obtaining a major in English with minors in Environmental Studies and Musical Theater. I graduated from Sewickley Academy in 2016 as a member of the Cum Laude Society with highest honors for all semesters. I am an AP Scholar with Honors, an Academic Al...
Princeton University
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5+ years
Anna
With each of my experiences working with children my passion for education has grown. I first came to Austin to work with a Spanish literacy intervention program through Americorps called A Community for Education (ACE). After my service with ACE I taught at a dual language (Spanish-English) school ...
Oberlin College
Bachelors, Comparative American Studies
The University of Texas at Austin
Current Grad Student, Communication Sciences and Disorders

Certified Tutor
10+ years
Deborah
My MA in English with a concentration in Rhetoric and Composition, together with my MA in Adult Education and Continuing Education, qualified me to have a stellar forty-three-year career as a full-time college professor predominately in the University System of Georgia. I have successfully instructe...
Georgia State University
Master of Arts, English
University of Missouri-Kansas City
Master of Arts, Adult and Continuing Education
University of Georgia
Bachelor in Arts, Political Science and Government

Certified Tutor
10+ years
Hi. I love math and I love teaching math. I am a state certified high school math teacher. I have 31 years of classroom experience. I currently teach Pre-Calculus and AP Statistics.
Clark Atlanta University
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Katherine
Hi, my name is Katherine and I've been tutoring in various capacities since 2012. Although I'm currently studying Computer Science at Swarthmore College, I have expertise in a number of subject areas and I'd love to help you out.
Swarthmore College
Current Undergrad Student, Computer Science

Certified Tutor
4+ years
Samantha
I believe every student has a unique learning skill set and every teacher continues to learn from her students. To ensure every student receives the best tutoring, I strive to offer excellent communication and a diverse set of teaching skills.I obtained my Bachelor in Business Administration from th...
University of Wisconsin-Whitewater
Bachelor in Business Administration, International Business/French
Vermont Law School
Juris Doctor, International Law

Certified Tutor
6+ years
Christopher
I am a current student at Rutgers University on track to major in Electrical Engineering. I tutor a wide range of math from elementary level up to high school and college. This range includes algebra, trigonometry, pre-calc and calculus. I have had many experiences through my high school and outside...
Rutgers University-New Brunswick
Bachelor of Engineering, Electrical Engineering

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Jerry
Hey, I enjoy teaching math, computer science, and the SAT! Contact me if you are interested in these.
The Texas A&M University System Office
Bachelor in Arts, Political Science and Government

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8+ years
Amy
I have a B.A. in French and a diploma in Business French from the Chamber of Commerce and Industry in Paris. I also speak Greek, Italian, and Spanish.I have worked as a private tutor in the area of foreign languages, essay writing, and a variety of other subjects for more than a decade. In that time...
Hofstra
Bachelor in Arts, French

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8+ years
Gabrielle
I am recent graduate of Binghamton University, with a Bachelor of Sciences in Biology. I am deeply committed to the value of education, and believe that learning is a gift and an opportunity for growth that should be available to everyone. For this reason, I am passionate about tutoring and helping ...
SUNY at Binghamton
Bachelor in Arts, Biology, General
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I am a graduate of LaSalle University in Mexico City. I received my Bachelor of Science degree inBusiness Administration with a focus on management. I am also a certifiedteacher of Spanish. Since graduation I have worked in Human Resources and I havealso been tutoring children and adults in private and public schools, as wellas online. I am very enthusiastic about teaching my native language because Ifeel that in that way I am enriching my students' education and experiences inlearning aspects of another culture. One area where we seem to have the mostfun is prepping for exams and writing assignments. I am a firm proponent ofeducation, and as a tutor, my approach is based on each of my students'level of proficiency, their goals, and their learning pace. I focus on providinga pleasant and safe experience for my students. I prepare lesson plans that arecreative and introduce new topics in a fun way, spending enough time reviewingthe material. Afterwards, I allow students time to practice on their own. I encourage you to contact me to schedule so togetherwe can start achieving your goals
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I honestly love tutoring. While working in finance and publishing over the past decade, I have independently tutored students from many premiere NY and NJ high schools and universities. I continued tutoring even after joining a major private equity firm because of how much I enjoy working one-on-one with students. Breaking down seemingly complex subjects is one of my favorite pastimes--it's part of the reason I also enjoy writing about arcane financial topics like quanto spreads on sovereign CDS. I've also developed a newfound respect for the challenges students face when undergoing years of testing after developing my own study plan to pass the first two CFA exams (I'm taking the third exam in June). This experience has shaped how I work with students to tackle test-taking anxiety and master difficult material quickly.I have both a BA and MA in English from New York University.
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Hello! My name is Catherine Raj and I am a second-year medical student at Ohio University Heritage College of Osteopathic Medicine. I graduated from The Ohio State University with a Bachelor's of Science in Neuroscience in 2022. Since 2015, I have tutored children from ages 3-16 in areas of math and reading, as well as their school curriculum. Apart from tutoring here, I have worked for the Kumon Learning Center as a teaching instructor for 5 years. While I am certified to tutor a broad range of subjects, I have years of experience with tutoring young children in math and reading, such as addition, subtraction, multiplication, division, phonics, reading comprehension, and much more. I connect with elementary and middle school students very well, as I believe in understanding children in order to give them a fulfilling tutoring experience. I also very much enjoy tutoring pre-algebra and algebra as those are my favorite math subjects, as well as my best! My students and I have always had a deeper level of understanding beyond the books and I pride my style of teaching on that aspect.
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I have been a special education teacher in Somerset County for the last 5 years. I have worked in self-contained classrooms and am currently working as a 4th grade resource room Reading and Math teacher. Next spring, I will graduate from Rutgers University's Graduate School of Education with an Ed.M in Reading Education. I will be a certified Reading Specialist as well as a certified supervisor. I am currently a certified Literacy Specialist.
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I love English, and good writing. Since I like working one-or-one or with a small group, tutoring is a great way for me to help young people communicate more effectively in writing. As a social scientist, I also like to talking about statistics and social science. I like to teach by example and ask lots of questions so students can discover answers themselves. When not working, I like to watch movies, exercise, and write science fiction.
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Living in Great New York Area since 2008. Graduate student at Columbia University.Major in Finance + Economics (Undergraduate Program), and Public Administration (Graduate Program), Average GPA is 3.65.Speak Mandarin, English and Japanese.Subjects cover East Asian History (China & Japan), International Relation, Public sector (NPO related).
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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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