1st lesson free
Emma
- Rate $58
- Response 1h
$58/hr
Contact
1st lesson free
- Maths
- Trigonometry
- Arithmetic
- Geometry
- Logic
Mathematics with 10 years of experience, covering real analysis, abstract algebra, number theory, and advanced proof-writing for research.
- Maths
- Trigonometry
- Arithmetic
- Geometry
- Logic
Lesson location
About Emma
Mathematics tutor with 10 years of experience teaching advanced high school and college students. Have successfully taught around 300 students, helping many prepare for competitive exams, university research projects, and graduate-level mathematics. My teaching philosophy is built on logical rigor and proof-based reasoning. I focus on building strong foundations in pure mathematics while developing advanced problem-solving and research skills. Notable achievements include helping over 40 students secure top ranks in national mathematics olympiads and guiding several to publish research papers. I create a supportive, intellectually challenging environment where questions are celebrated. I keep detailed records of each session to track progress and adjust methods as needed. Whether you are preparing for competitive exams or pursuing research, I tailor every lesson to your specific goals.
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About the lesson
- Primary
- High School
- NCEA Level 1
- +5
levels :
Primary
High School
NCEA Level 1
NCEA Level 2
NCEA Level 3
Adult education
Masters
Doctorate
- English
All languages in which the lesson is available :
English
My teaching approach for Mathematics and related subjects is built on logical rigour, abstraction, and proof-based reasoning. I connect every advanced theorem to its foundational axioms, so you understand the structure of mathematics. We break down topics like real analysis, abstract algebra, and topology into clear, deductive steps. I encourage creative thinking by asking you to construct proofs and explore counterexamples. Motivation comes from setting research-style goals and celebrating each elegant proof. Integrity means I give honest feedback, never accept vague reasoning, and always adapt to your learning style. For Mathematics, we cover real analysis (sequences, series, continuity, differentiation, Riemann integration), abstract algebra (groups, rings, fields, Galois theory), topology (metric spaces, compactness, connectedness), number theory (divisibility, congruences, elliptic curves), and complex analysis. We also work on mathematical logic, set theory, and category theory basics. I also teach related subjects that support your math mastery: Physics for Math – applications in quantum mechanics and relativity. Computer Science for Math – algorithms, cryptography, and computational complexity. Philosophy for Math – foundations and philosophy of mathematics. In every lesson, I use case studies from pure mathematics and my own students. For example, I show how one student mastered group theory using a visual symmetry approach, then we apply that to your current problems. I share stories of students who improved by writing daily proofs. My sessions are rigorous and interactive. We construct proofs, discuss counterexamples, explore mathematical structures, and solve advanced problems. I assign homework like proving key theorems, solving complex problems, or writing a mini-research paper. I adapt my pace to your goals, whether for exams, research, or intellectual growth. I never compare you to others, only to your previous self. I keep detailed notes of each lesson so we always build on what we did before. My goal is to make you a confident, rigorous, and creative mathematician.
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Rates
Rate
- $58
Pack prices
- 5h: $291
- 10h: $582
online
- $58/h
free lessons
The first lesson with Emma will allow you to get to know each other and discuss your needs for future lessons.
- 1hr
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