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Award-Winning Commutative 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
Jane

Certified Tutor

8+ years

Jane

Current Undergrad Student, English
Jane's other Tutor Subjects
ACT Prep
ACT English
ACT Math
ACT Reading

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...

Education

Princeton University

Current Undergrad Student, English

Test Scores
SAT
1540
ACT
34
Anna

Certified Tutor

5+ years

Anna

Current Grad Student, Communication Sciences and Disorders
Anna's other Tutor Subjects
ACCUPLACER ESL - Listening
ACCUPLACER ESL - Reading Skills
ACCUPLACER ESL - Sentence Meaning
ACCUPLACER Language Use

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 ...

Education

Oberlin College

Bachelors, Comparative American Studies

The University of Texas at Austin

Current Grad Student, Communication Sciences and Disorders

Deborah

Certified Tutor

10+ years

Deborah

Master of Arts, English
Deborah's other Tutor Subjects
6th Grade AP Language Composition
ACT Writing
Business
Business Writing

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...

Education

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

Deborah

Certified Tutor

10+ years

Deborah

Bachelor of Science, Mathematics
Deborah's other Tutor Subjects
Algebra
Algebra 2
Geometry
Math

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.

Education

Clark Atlanta University

Bachelor of Science, Mathematics

Katherine

Certified Tutor

Katherine

Current Undergrad Student, Computer Science
Katherine's other Tutor Subjects
ACT Science
ACT Writing
Adult Literacy
AP Computer Science Principles

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.

Education

Swarthmore College

Current Undergrad Student, Computer Science

Test Scores
SAT
1530

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Samantha

10th Grade Reading Tutor • +119 Subjects

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 the University of Wisconsin - Whitewater where I double majored in International Business and French. I also obtained my paralegal certificate and minored in Legal Studies. After my undergraduate program, I earned my Juris Doctorate from Vermont Law School where I specialized in International Environmental Treaties. I also obtained my certificate in Comparative Legal Systems.I began working as a child care provider in 1998 and continued until I graduated from Law School. I also worked as a para-educator for down-syndrome children in Vermont public schools. For the past four years, I have taught at the collegiate level. I have taught many subjects including legal research and writing, political science, professional development, college career and success, sociology, computer science, English, ethics, and accounting.Besides my formal education, I have a diverse arts background, including Voice, French Horn, and Dance. I enjoy many sports including ice skating, hiking, skiing, and biking. I am currently learning photography. Lastly, I am an avid volunteer in my community. In particular, I provide event management, planning, and fundraising support to Animal Aid, the Girl Scouts, Well Arts, and Humane Educators Reaching Teachers (HEART).From this diverse background, I offer tutoring in English, Literature, Accounting, French, Voice, Elementary and Middle School Math, Phonics, Political Science, Legal Studies, LSAT Prep, Study Skills, Science, and Public Speaking.For my full work history and credential, please feel free to visit my LinkedIn page at: www.linkedin.com/pub/samantha-balmes/50/326/a0a/

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Christopher

Algebra Tutor • +7 Subjects

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 work at kumon learning centers in tutoring. I love helping students not only learn the material themselves, but being able to know it well enough that they can teach it themselves, achieving my goal of getting students to work autonomously without required help. The many interests I have outside of the classroom includes playing basketball, running, video games, and computer programming.

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Jerry

ACT Writing Tutor • +2 Subjects

Hey, I enjoy teaching math, computer science, and the SAT! Contact me if you are interested in these.

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Amy

College English Tutor • +13 Subjects

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, I have witnessed the difficulties many students have when learning something that seems unfamiliar, uninteresting, or just makes no sense. Seeing this, I believe it is my responsibility to be a positive influence by ensuring that all my students do well and understand the material. For example, with French, I always give them a brief English grammar lesson beforehand which helps tremendously boost their confidence level as the foreign gradually becomes familiar.I am truly excited about working with students and encouraging them to excel. There is nothing more gratifying than seeing a student conquer his/her fears and expressing him/herself in a way he/she never thought possible. I work with each student’s specific needs in a patient yet firm manner. I also exhibit determination, empathy, and humor to make learning an enjoyable and rewarding experience. Most importantly, I am personable and understanding and believe that brings me closer to helping my students.In my free time, I love cooking Mediterranean/Greek cuisine and would love to open a restaurant one day. I also write poetry, short stories, etc. and am currently working on my first novel. Lastly, I adore knitting and crocheting cute, fashionable clothes and accessories for girls.

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Gabrielle

AP Biology Tutor • +25 Subjects

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 students, so that everyone is able to not only do well in school, but to fall in love with learning in the process. Anyone can enrich themselves through learning. This is the foundation of my teaching philosophy: in addition to emphasizing results and academic achievement, I believe it is integral to find an individual approach to each student and to focus first and foremost on teaching students to study in a way that is effective and engaging. I tutor elementary, middle, and high school students in all subjects. In my free time, I like to go running, practice dance, learn new languages, and play ping-pong.

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Julie

Languages Tutor • +4 Subjects

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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Anna

ACT Writing Tutor • +27 Subjects

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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Catherine

Algebra Tutor • +15 Subjects

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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Grace

ACCUPLACER Arithmetic Tutor • +22 Subjects

I am a graduate of Harvard Graduate School of Education (3.95 GPA) and New York University (3.98 GPA). I have worked with students of all ages. I love adapting my teaching style to the individual needs of each student to help them fulfill their greatest potentials.

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Sarah

Elementary School Math Tutor • +20 Subjects

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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Frequently Asked Questions

Students often find the transition from polynomial rings to abstract ring theory challenging—particularly understanding ideals, quotient rings, and localization. Many struggle with Noetherian rings and primary decomposition, where the intuition from linear algebra doesn't directly apply. Another common pain point is grasping why certain properties (like unique factorization) hold in some rings but not others, and how to work with modules over non-principal ideal domains. Tutors help students build the conceptual framework needed to see these structures as natural extensions of familiar algebraic objects.

Commutative algebra proofs often require identifying which ring properties are relevant and knowing when to apply tools like the Chinese Remainder Theorem, Nakayama's Lemma, or localization. Tutors help you develop a strategic approach: recognizing proof patterns (contrapositive arguments, contradiction, induction on degree), knowing when to reduce to local rings, and understanding how to leverage prime ideals as a diagnostic tool. Working through proofs together, you'll learn to ask the right questions—like "Is this property preserved under localization?" or "Can I reduce to the case where the ring is local?"—that guide your problem-solving.

Ideals are abstract by nature, and it's easy to manipulate them symbolically without understanding what they represent geometrically or algebraically. Many students struggle to see why prime ideals correspond to irreducible varieties, or why maximal ideals are the "points" of a ring's spectrum. Tutors bridge this gap by connecting ideals to concrete examples—like how ideals in polynomial rings relate to solution sets of equations—and by building intuition through worked examples before moving to general theorems. This conceptual grounding makes advanced topics like primary decomposition and localization much more accessible.

Localization often feels like an unmotivated technique until you see it solves real problems. The key insight is that localizing at a prime ideal focuses your attention on that prime—making properties "local" easier to verify than globally. Tutors help you recognize when localization is the right tool: checking if a module is projective, understanding flatness, or reducing global problems to local ones where intuition is clearer. By working through examples where localization simplifies a proof or reveals structure, you develop the judgment to apply it strategically rather than mechanically.

Noetherian rings are significant because they guarantee that ascending chains of ideals stabilize—a property that makes many theorems possible and prevents pathological behavior. Students often miss why this matters until they see examples of non-Noetherian rings where basic results fail. Tutors help you appreciate Noetherian rings by contrasting them with counterexamples, showing how the Noetherian condition enables primary decomposition and makes dimension theory well-behaved. Understanding this foundational property transforms how you approach problems: you'll recognize when Noetherian assumptions are doing the heavy lifting in a proof.

Modules generalize vector spaces by allowing scalars from a ring rather than a field, but this added generality introduces subtleties: modules over non-principal ideal domains don't have nice basis decompositions, and properties like projectivity and flatness replace simpler linear algebra intuitions. Students often struggle because module-theoretic arguments feel less concrete than polynomial ring calculations. Tutors help by showing how modules arise naturally in commutative algebra—like using modules to study homological properties of rings—and by building intuition through examples before tackling general theorems about projective, flat, or free modules.

Dimension theory in commutative algebra is defined through chains of prime ideals rather than geometric dimension, making it feel disconnected from intuition. Students struggle because Krull dimension, height, and depth are defined algebraically, and it's unclear why these definitions capture what we mean by "dimension." Tutors help by connecting these definitions to geometric intuition—showing how chains of primes correspond to irreducible subvarieties—and by working through concrete examples in polynomial rings where algebraic definitions align with geometric intuition. Once you see this connection, dimension-theoretic arguments become much more interpretable.

Commutative algebra textbooks vary significantly in style—some emphasize homological methods, others focus on geometric intuition, and some prioritize computational aspects—which can create gaps in understanding when switching between sources. Tutors help by providing a coherent narrative that connects these perspectives, filling in skipped steps, and translating between different notational conventions. They can also guide you on which foundational concepts to prioritize based on your goals, whether that's algebraic geometry, number theory, or homological algebra, ensuring you build the right intuitions for your specific needs.

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