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Griffin
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...
Kansas State University
Bachelor of Science, Chemical Engineering
Certified Tutor
6+ years
Ian
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...
University of Georgia
Current Undergrad Student, Accounting
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6+ years
Samantha
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.
Middle Georgia State University
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Aiden
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.
Reed College
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Jack
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.
Northeastern University
Bachelor of Science, Physics
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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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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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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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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
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Rice University
Doctor of Philosophy, Mechanical Engineering
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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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Frequently Asked Questions
Many students struggle with the shift from concrete arithmetic to abstract algebraic structures. Common pain points include understanding why associativity matters in different contexts (matrices don't commute, but they do associate), manipulating expressions with nested parentheses, and recognizing when the associative property applies versus when it doesn't. Students also often find it difficult to work with non-commutative operations and to understand how associative algebras relate to linear algebra and group theory. A tutor can help clarify these distinctions and build intuition for why these properties matter in advanced mathematics.
Rather than treating the associative property as an isolated rule to memorize, tutors help students see it as a fundamental structural property that enables consistent computation. This involves working through concrete examples—like how matrix multiplication is associative but not commutative, or how string concatenation differs from number addition—to build conceptual understanding. Tutors also guide students through proofs and derivations so they see *why* associativity holds in specific algebraic systems, not just that it does. This approach helps students recognize patterns across different algebras and apply the concepts to new problems they haven't seen before.
In associative algebra, the steps you take matter because they reveal your understanding of how elements interact and why certain manipulations are valid. Showing work helps tutors identify whether you're applying associativity correctly, confusing it with commutativity, or making computational errors. It also forces you to justify each step—which is essential in abstract algebra where intuition alone isn't enough. When you write out your reasoning, you're building the habit of rigorous mathematical thinking that's critical for success in higher-level courses.
An effective tutor understands not just the computational mechanics but the deeper theory—how associative algebras fit into linear algebra, group theory, and ring theory. They should be able to explain concepts at multiple levels of abstraction, moving fluidly between concrete examples (like 2×2 matrices) and general principles. Strong tutors also recognize common misconceptions (like assuming all operations are commutative) and can address them directly. Finally, they should be comfortable with proofs and mathematical reasoning, since understanding *why* something is true is central to mastering associative algebra.
For students new to the subject, tutors focus on building foundational understanding of what makes an operation associative and how this differs from other properties like commutativity and distributivity. For intermediate students, tutors dive deeper into specific algebraic structures—quaternions, matrix algebras, group algebras—and how to work within them. Advanced students benefit from tutors who can help with proofs, connections to other areas of mathematics, and problem-solving strategies for complex multi-step questions. Tutors personalize the pace and depth based on where you are, ensuring you're always building on solid ground.
Associative algebra doesn't exist in isolation—it's deeply connected to linear algebra (matrices form associative algebras), group theory (groups are associative), and ring theory (rings require associativity). A tutor helps you recognize these connections by showing how the same structural principles appear across different contexts. For example, understanding associativity in matrix multiplication helps you see why certain algebraic manipulations work in group algebras. These connections not only deepen your understanding but also make problem-solving more intuitive, since you can draw on insights from related areas.
Abstract algebra can feel intimidating because the objects you're working with—like algebras themselves—are less concrete than numbers. Tutors reduce this anxiety by grounding abstract ideas in tangible examples first, then gradually building to more general theory. They also normalize the struggle; abstract thinking is genuinely difficult, and slowing down to understand each piece thoroughly is the right approach, not a sign of weakness. Regular practice with a tutor who explains the 'why' behind concepts builds confidence because you're not just following rules—you're understanding the logic underneath.
Effective proof strategies include starting by identifying what you need to show, working backward from the conclusion to see what would imply it, and using the associative property strategically to regroup terms. Many students benefit from learning to recognize proof patterns—like using associativity to combine terms, applying definitions systematically, and organizing multi-step arguments clearly. Tutors teach you to ask questions like "Can I use associativity here to simplify?" and "What property would let me rewrite this expression?" These strategies transform proofs from mysterious puzzles into manageable, logical sequences.
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