1st lesson free
Miles
- Price $53
- Answer 1h
$53/h
Contact
1st lesson free
- Maths
- Trigonometry
- Arithmetic
- Geometry
- Statistics
Master Arithmetic & Trigonometry with Expert Guidance – 8 Years’ Experience Offering Tailored Lessons to Deepen Understanding, Build Confidence, Sharpen Skills, and Ensure Every Student Achieves Exam
- Maths
- Trigonometry
- Arithmetic
- Geometry
- Statistics
Lesson location
About Miles
My lessons open the door to the elegant and challenging world of advanced theoretical mathematics. With a gentle and reflective approach, I guide students through abstract algebra, number theory, mathematical proofs, and other higher-level concepts. Each session is designed to build not just knowledge, but the ability to think independently and reason with precision. We explore the deep structures that lie beneath familiar mathematics, uncovering patterns and connections that inspire curiosity. In abstract algebra, we investigate groups, rings, and fields, seeing how they shape the logic of mathematics. In number theory, we discover the surprising beauty hidden in prime numbers, modular arithmetic, and Diophantine equations. The rigor of proofs is central to our journey, but I break each argument into clear, understandable steps. I use relatable examples and analogies to make abstract ideas easier to grasp without losing their depth. Students are encouraged to question, experiment, and form their own interpretations of complex theorems. Whether preparing for academic advancement or pursuing personal enrichment, learners find a space here to grow at their own pace. My aim is to help each one excel in both skill and understanding. Together, we will uncover the elegance at the heart of mathematical thought and see how it shapes the way we understand the world.
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About the lesson
- Primary School
- High School
- Year 10
- +8
levels :
Primary School
High School
Year 10
Year 11-12
Year 12
TAFE
Adult
Undergraduate
Diploma/Certificate
PhD
Early childhood education
- English
All languages in which the lesson is available :
English
With over 8 years of teaching experience and a BSc in Statistics and Mathematics, I specialize in making the abstract foundations of mathematics approachable and engaging. My passion lies in helping advanced high school and early university students grasp concepts that often seem intimidating at first glance. I focus on set theory, cardinality, axiomatic systems, and the art of formal proofs, guiding learners through ideas that form the very core of mathematical reasoning.
Through carefully chosen analogies and clear step-by-step explanations, I turn abstract definitions into relatable mental models. I’ve worked extensively with students pursuing pure mathematics, logic, and theoretical computer science, helping them develop precision in thinking and expression. My lessons balance rigor with accessibility, ensuring that students not only solve problems but also understand why the methods work.
We explore how infinite sets compare in size, why axioms are the starting point of all mathematical structures, and how proofs act as the language of truth in mathematics. By breaking down complex concepts into logical progressions, I empower students to build both confidence and independence.
Mathematics, in its purest form, is a journey into the structure of thought itself. I’m here to make that journey not only possible but deeply rewarding. Let’s explore together the bedrock of mathematical thought and discover the elegance that lies beneath every theorem.
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Rates
Price
- $53
Pack prices
- 5h: $265
- 10h: $530
online
- $53/h
free lessons
The first lesson with Miles will allow you to get to know each other and discuss your needs for future lessons.
- 1hr
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