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I am a licensed physician from Florida who is currently changing careers. I graduated from the University of Pennsylvania in 2009 and have extensive tutoring and editing experience. While a student, I became a certified writing tutor through the Critical Writing Department. Since I completed my writ...
Nova Southeastern University
PHD, Medicine
University of Pennsylvania
Bachelors, History
University of Pennsylvania
undergraduate
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9+ years
Jai
I'm a recent Stanford graduate (Electrical Engineering and Computer Science), and have been working at a major Management Consulting firm for a few years now. I personally scored a 2360 (out of 2400) on the SAT and 35 on the ACT and was successful in gaining admission to several top universities. I'...
Stanford University
Bachelors in Electrical Engineering and Computer Science
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Kate
I'm available to tutor biology, chemistry, physics, math from Algebra up through AP Calculus, SAT test prep, and French. I've been tutoring students in science and math for 7 years. I also spent 8 months working and studying in France, and have tutored high school and adult students in French. When ...
Massachusetts Institute of Technology
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Massachusetts Institute of Technology
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Erika
I am available to tutor middle and high school math, history and test prep. I have tutored math and history in the past and I previously taught a test prep course at a school in Hanoi, Vietnam. I have a lot of experience teaching all the need-to-know tricks to doing great on the SATS/ACTS! When I am...
Harvard University
Master of Public Policy, Public Policy
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6+ years
Rhea
I am a current student at the University of Chicago. I am working towards a Bachelor of Science in Biological Sciences, and I am on the pre-medical track. I am extremely passionate about tutoring, and I have several years of experience tutoring students in my high school's learning center in various...
University of Chicago
Bachelor of Science, Biology, General
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6+ years
Jeffrey
I am enrolled in the Mechanical Engineering PhD program at Rice University which will begin Fall 2020, and I am hoping to return to academia as a professor after earning my PhD. In the meantime, I am looking to share my passion for gaining knowledge, specifically in STEM, by educating the up and com...
University of Notre Dame
Bachelor of Science
Rice University
Doctor of Philosophy, Mechanical Engineering
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9+ years
Sami
I am a Duke University graduate in Economics and Computer Science. I am currently pursuing an MBA degree at the Yale School of Management. I have worked in the financial field, both at a management consulting firm and a fortune 500 company. My hobbies include playing and coaching soccer.
Duke University
Bachelor of Science (Economics and Computer Science)
Yale School of Management
Current Undergrad Student, Business Administration and Management
Certified Tutor
9+ years
Sharon
I am a graduate of the University of Chicago, and I will be starting a graduate program at Columbia in August. I am about to complete a year of service with City Year, an education non-profit that places young adults into under-served schools. As a City Year member, I worked full-time in the classro...
Columbia University in the City of New York
Master of Science, Journalism
University of Chicago
Bachelor in Arts
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9+ years
Annie
I am currently a second year medical student. I was a Physiological Sciences major at UCLA (class of 2015), and pursued research during my gap year between undergrad and medical school.
University of California Los Angeles
Bachelors, Physiological Sciences
Drexel University College of Medicine
Current Grad Student, MD
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Tony
I am a recent graduate of Yale University and incoming first year medical student at Columbia University. Originally from the DC area, I have always had a passion for science and medicine and pursued a degree in Biology while at Yale. During the 2008-2009 academic year, I tutored science, math, Engl...
Yale University
Bachelor of Science in Biology
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Matthew
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I'm a highly creative person who works best with visual thinkers. Very recently graduated from Stanford University, I majored in Human Biology with a concentration in Bioinformatics and Stem Cell Science. Technical though my background may be, I am currently gigging as a singer/songwriter/composer in NYC and tackle even the most hard-science of problems with a top-down, big-picture, holistic approach. If you have a propensity to look at problems in a cross- or inter-disciplinary manner (or want to learn how to do so), I'm the tutor for you!
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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 describe my tutoring style as one that adapts to each students' needs. For example, I have always tried to frame questions in a different way so that the student can better understand the question. Some students need visual representations of numbers and systems to understand them, and others benefit more by understanding the concepts behind each formula. I prefer to tutor in math and physics, and especially with real world application problems. I hope to help students improve their standardized test scores and their understanding of the math and sciences so that they can achieve their academic goals! Hobbies: art, books, running, reading, music, writing
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I am a freshman at Caltech majoring in Applied and Computational Mathematics. My favorite subject to tutor is math because I find it very rewarding to simplify complex topics to aid in understanding. I have lots of tutoring experience. In high school, I ran and taught an SAT prep class and was vice president of my school's NHS chapter where I ran our tutoring program, and I, myself, tutored. I also was a teaching assistant in the summer of 2020 for a class in discrete mathematics through a program called PACT (Program in Algorithmic and Combinatorial Thinking). I love learning and hope to make the process enjoyable for you!
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Frequently Asked Questions
Students often find finite geometry challenging when transitioning from Euclidean geometry because it requires thinking about non-traditional spaces and structures. Common trouble spots include understanding incidence geometry (how points and lines relate in finite planes), working with finite fields and their properties, grasping affine and projective planes, and applying combinatorial reasoning to geometric problems. Many students also struggle with proofs in finite geometry because they require both abstract thinking and careful logical construction—skills that differ from coordinate geometry or traditional Euclidean proofs.
A tutor can break down abstract finite geometry concepts by starting with concrete examples—like small finite planes or specific incidence structures—before moving to general theory. This helps you see patterns and connections that make definitions like "a finite projective plane of order n" feel less intimidating. Tutors can also use visual representations, guided problem-solving to show how axioms lead to specific conclusions, and practice with proofs that build confidence in logical reasoning. Working through examples where you construct your own finite geometries reinforces why the rules matter.
Finite geometry proofs often require you to use axioms about incidence (like "any two distinct points determine a unique line") systematically. Effective strategies include: listing what the axioms guarantee, identifying what you need to prove, and building a logical chain that connects them. Tutors can help you recognize proof patterns—such as counting arguments, contradiction proofs, or induction on the order of a structure—that appear repeatedly in finite geometry. Practice with structured proof templates also helps you develop the habit of justifying each step clearly, which is essential when working in non-intuitive spaces.
Finite geometry is fundamentally about counting and structure: in a finite projective plane of order n, there are exactly n² + n + 1 points and the same number of lines, with each line containing n + 1 points. Understanding these combinatorial relationships helps you verify whether a structure is valid and predict properties without constructing the entire geometry. Tutors emphasize this connection by showing how counting arguments prove theorems and how combinatorial constraints shape the geometry itself—this perspective transforms finite geometry from abstract rules into a cohesive system where everything connects.
Finite geometry abandons familiar assumptions like "there are infinitely many points on a line" or "parallel lines never meet." In finite geometries, especially projective planes, parallel lines don't exist—every pair of lines intersects at exactly one point. This shift requires you to let go of intuition built from Euclidean space and instead rely on axioms and logical deduction. A tutor helps by explicitly contrasting finite and Euclidean systems, showing why familiar intuitions fail, and building new mental models based on the actual axioms you're working with—this makes the abstract feel purposeful rather than arbitrary.
Finite geometry appears in coding theory (error-correcting codes use finite geometries to maximize information), cryptography, design theory (creating balanced experimental designs), and even network design. Learning that finite projective planes are used to construct efficient communication systems or that finite geometries help organize tournaments and schedules makes the abstract theory feel relevant. Tutors often reference these applications when introducing concepts, helping you see why mathematicians care about these structures and giving you context for why specific properties matter—this bridges the gap between abstract axioms and real problem-solving.
Finite geometry can feel intimidating because it's often your first encounter with truly abstract mathematics, but confidence builds through mastery of fundamentals: understanding what axioms are, practicing small examples until they feel familiar, and seeing that theorems follow logically from axioms. Tutors help by celebrating small wins—like successfully constructing a finite plane or completing your first proof—and by showing you that struggling with abstraction is normal and temporary. Regular practice with increasingly complex problems, combined with a tutor who explains the "why" behind each concept, transforms confusion into competence.
Exam preparation should emphasize mastering the axioms and definitions specific to your course (affine vs. projective planes, finite fields, incidence structures), practicing proofs that combine multiple concepts, and working through problems that require you to apply theory to novel situations. Tutors recommend creating summary sheets of key theorems and their proofs, practicing proof-writing under timed conditions, and reviewing common mistakes from problem sets. Many exams also test your ability to construct examples, verify properties, or explain why a structure satisfies certain axioms—so practice articulating your reasoning clearly, not just getting the right answer.
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