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Award-Winning Multilinear algebra Tutors

Griffin

Certified Tutor

6+ years

Griffin

Bachelor of Science, Chemical Engineering
Griffin's other Tutor Subjects
6th-12th Grade Algebra
6th Grade Calculus
Middle School Math
Polynomials

I am a graduate from Kansas State University with a B.S. in Chemical Engineering. I have worked professionally as a research assistant for KSU, a project manager for Cargill, and an auxiliary engineer with Black & Veatch. With recent experience in office, industry, and university, I am fully prepare...

Education

Kansas State University

Bachelor of Science, Chemical Engineering

Test Scores
ACT
34
Ian

Certified Tutor

6+ years

Ian

Current Undergrad Student, Accounting
Ian's other Tutor Subjects
9th-12th Grade Algebra
AP Statistics
Statistics
Calculus

I am an undergraduate student in my junior year at the University of Georgia. It is currently my second semester in the Tull School of Accounting here and I plan on pursuing a Masters of Accountancy in the graduate program. I have years of experience tutoring during my time as a member of a Math Hon...

Education

University of Georgia

Current Undergrad Student, Accounting

Test Scores
SAT
1500
Samantha

Certified Tutor

6+ years

Samantha

Associate in Arts, Political Science and Government
Samantha's other Tutor Subjects
6th-12th Grade Algebra
Middle School Math
Calculus
Polynomials

I am currently working towards a Political Science degree with a focus in Statistics, and I hope to go on to law school after I graduate. My favorite subjects are Statistics, Political Science, History, English, and French.

Education

Middle Georgia State University

Associate in Arts, Political Science and Government

Test Scores
SAT
1430
Aiden

Certified Tutor

6+ years

Aiden

Bachelor in Arts, Political Science and Government
Aiden's other Tutor Subjects
6th-12th Grade Algebra
Middle School Math
Calculus
Elementary School Math

I'm a recent graduate from Reed College where I majored in Political science with additional concentrations in environmental science, sociology, philosophy, and 3D art.

Education

Reed College

Bachelor in Arts, Political Science and Government

Test Scores
ACT
33
Jack

Certified Tutor

6+ years

Jack

Bachelor of Science, Physics
Jack's other Tutor Subjects
6th-12th Grade Algebra
6th-12th Grade Calculus
Polynomials
Linear Systems

I am a Junior in college at Northeastern University working towards my Bachelor of Science in Physics. I aspire to earn my PhD in Physics after college.

Education

Northeastern University

Bachelor of Science, Physics

Test Scores
SAT
1490
Jessica

Certified Tutor

Jessica

PHD, Medicine
Jessica's other Tutor Subjects
College Algebra
Calculus
Algebra
Honors Chemistry

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...

Education

Nova Southeastern University

PHD, Medicine

University of Pennsylvania

Bachelors, History

University of Pennsylvania

undergraduate

Test Scores
SAT
1540
Jai

Certified Tutor

9+ years

Jai

Bachelors in Electrical Engineering and Computer Science
Jai's other Tutor Subjects
Calculus
Algebra
Electrical Engineering
ACT Writing

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'...

Education

Stanford University

Bachelors in Electrical Engineering and Computer Science

Test Scores
SAT
1590
ACT
35
Kate

Certified Tutor

Kate

Masters, Environmental Engineering
Kate's other Tutor Subjects
AP Calculus BC
AP Calculus AB
College Algebra
Pre-Calculus

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 ...

Education

Massachusetts Institute of Technology

Masters, Environmental Engineering

Massachusetts Institute of Technology

Bachelors

Test Scores
SAT
1580
Erika

Certified Tutor

Erika

Master of Public Policy, Public Policy
Erika's other Tutor Subjects
Pre-Algebra
Middle School Math
Calculus
Algebra

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...

Education

Harvard University

Master of Public Policy, Public Policy

Test Scores
ACT
32
Rhea

Certified Tutor

6+ years

Rhea

Bachelor of Science, Biology, General
Rhea's other Tutor Subjects
AP Statistics
AP Calculus BC
AP Calculus AB
Pre-Algebra

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...

Education

University of Chicago

Bachelor of Science, Biology, General

Test Scores
Perfect Score
SAT
1550
ACT
36

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Jeffrey

Pre-Calculus Tutor • +29 Subjects

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 coming members of such a great field. I have experience tutoring both Calculus and Physics at Notre Dame, as well as experience as a Student Assistant for Differential Equations and Mechanics. I believe the key to learning is much deeper than learning to solve problems and that seeking knowledge is one of the best means for personal improvement.

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Sami

Pre-Algebra Tutor • +19 Subjects

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. Hobbies: reading, writing, art, books, music

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Sharon

Pre-Algebra Tutor • +29 Subjects

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 classroom with middle-school students who were in approximately the 10th percentile for math (meaning they score lower than 90% of students). One-fourth of those students were able to grow around 15 percentile points by the end of the year! Hobbies: reading, cooking, gardening, music, art, nature, books, writing

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Annie

Pre-Algebra Tutor • +28 Subjects

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.

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Tony

Calculus Tutor • +28 Subjects

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, English, history, and Mandarin Chinese part-time with a DC-based tutoring company. At Yale, I worked as a freshman counselor to provide academic and career advice to incoming freshmen. I have taken both SAT and MCAT test prep classes and am familiar with both tests as well as the preparation necessary to score well. My personal career goals include attending medical school to pursue either immunology/infectious diseases or psych/neurology, teaching biology at the university level, and working in public/global health with either the CDC or the WHO.

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Matthew

Pre-Algebra Tutor • +39 Subjects

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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Charles

AP Calculus AB Tutor • +25 Subjects

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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Tiffany

Pre-Algebra Tutor • +56 Subjects

I am available to tutor a broad range of subjects, I am passionate about test preparation, Accountancy, and Algebra.

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MaryAnn

Calculus Tutor • +21 Subjects

I am a published author who has enjoyed “coaching” our daughter, as she navigated through high school, college and graduate school. I mentor college juniors who are seeking careers in financial services, and I serve as a peer resource to professionals who are transitioning from private industry to the nonprofit sector. Hobbies: reading, cooking, writing, books, music, art, travel

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Samuel

AP Calculus AB Tutor • +29 Subjects

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

Multilinear algebra extends linear algebra by studying functions and mappings that are linear in each of their arguments separately. It's challenging because it requires shifting from thinking about single vectors and matrices to reasoning about higher-dimensional structures like tensors, multilinear maps, and alternating forms. Students often struggle with the abstract nature of the material and how these concepts connect to the linear algebra they already know. A personalized tutor can help you build intuition by breaking down these abstract ideas into concrete examples and showing how multilinear concepts build naturally from linear algebra foundations.

Multilinear algebra is foundational for numerous advanced fields including functional analysis, differential geometry, representation theory, and algebraic topology. It's also essential for applications in physics, computer science (especially machine learning and data science), and engineering. Understanding tensor products, wedge products, and multilinear forms gives you the mathematical language needed for these disciplines. A tutor experienced in multilinear algebra can help you see these connections clearly, showing you how mastering these concepts opens doors to deeper mathematical understanding and practical applications.

Students typically struggle with: (1) understanding why tensor products work the way they do and their universal property, (2) grasping the difference between the tensor product and other operations like direct sum or Cartesian product, (3) visualizing multilinearity in higher dimensions, and (4) working with alternating forms and exterior algebra. Many students can compute with these objects but lack the conceptual foundation for why those computations matter. Personalized instruction helps you move beyond procedural understanding to see the underlying patterns—a key shift that transforms multilinear algebra from confusing symbols into coherent mathematical ideas.

Multilinear algebra is taught differently depending on your program's focus. Some textbooks introduce it through tensor products first (the universal property approach), while others emphasize alternating forms and exterior algebra. Physics-oriented texts often lead with component notation and index conventions, while pure math texts prioritize abstract definitions and categorical thinking. Your curriculum might also emphasize applications to differential forms, representation theory, or computational methods. A tutor who understands various approaches can translate between them, helping you make sense of your specific textbook while building flexibility in how you think about these concepts.

You should be comfortable with linear algebra fundamentals: vector spaces, linear maps, matrices, eigenvalues/eigenvectors, and ideally some exposure to abstract thinking about linear transformations rather than just computation. A solid understanding of quotient structures, direct sums, and dimension theory is particularly helpful. If your linear algebra background is shaky or mostly procedural (just computing), a tutor can help you build those conceptual foundations first. Strong multilinear algebra depends less on computational skill and more on your ability to think abstractly about structure, so personalized instruction focused on understanding—not just problem-solving—is especially valuable here.

Effective multilinear algebra problem-solving relies on recognizing structural patterns and knowing which tools apply to each situation. A tutor helps you develop a toolkit of strategies: when to use the universal property, how to leverage bilinearity to break complex problems into pieces, when to switch between abstract and coordinate representations, and how to visualize relationships between tensor spaces. The best approach involves working through problems together, talking through your thinking process, and learning to ask the right structural questions before diving into computation. This builds mathematical maturity—the ability to see why an approach will work before executing it—which is far more valuable than memorizing solution methods.

With personalized instruction, you can expect to: develop genuine understanding of tensor products and why they're constructed the way they are, master alternating forms and exterior algebra with confidence, see clear connections between different topics in the course, improve your ability to work with abstract definitions and proofs, and build mathematical maturity that prepares you for advanced topics. Many students report that concepts that seemed impossibly abstract suddenly "click" when explained by someone who understands both the material and where students typically get stuck. The goal isn't just passing the course—it's developing the conceptual foundation and confidence you need for whatever advanced mathematics comes next.

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