Information about Harrison - Mornington tutor

Personal Description:

I tutor maths so I can support myself while I study maths.
Put simply, I love Maths.

I've studied and tutored Applied Mathematics for over 10 years. I'm currently studying Pure Mathematics and Software Engineering at university. I've also studied several years of Electrical and Computer Systems Engineering at university. This considerable experience has refined my skills in conveying complex knowledge in a simple, concise, and engaging way.

I believe Mathematics offers us an escape that cannot be found elsewhere. It allows us to feel safeguarded while still engaging with the world around us in a meaningful and productive way. It's my sincere hope to inspire passion in my students and teach them the right way to engage with this fascinating subject.

I'm a big fan of quantum mechanics, general relativity, metaphysics, epistemology, and unsolved mysteries. I enjoy watching cop camera footage, live court cases, and quality cooking shows like MKR and Hells Kitchen. I also enjoy watching AFL and european soccer.

Tuition Experience:

Over the years I've tutored students in a wide range of mathematical areas… LOGIC AND PROOFS
Propositional and first order logic, combinational and sequential logic, direct proof, proof by induction, strong induction, contradiction, contraposition, sets, multisets, equivalence relations, modular arithmetic, injections, surjections, bijections, the pigeonhole principle, and the Cantor–Schroder–Bernstein theorem.

DIFFERENTIAL EQUATIONS
First and second order ODEs, higher order ODEs, homogenous and nonhomogeneous ODEs, systems of ODEs, PDEs, the wave equation, the heat equation, the LaPlace equation, dilution, flow, radioactive decay, chemical reactions, Newton's Law of Cooling, the logistic equation, population growth, investing money, Euler's method, and numerical solutions.

VECTOR CALCULUS
Dot and cross product, vector identities, geometric vector proofs, lines and planes, scalar and vector fields, nonlinear coordinate systems (polar, cylindrical, and spherical), grad, div, curl, flux, space curves, curvature, torsion, parametric surfaces, line and surface integrals, Green's Theorem, Stokes theorem, the divergence theorem, kinetics, kinematics, projectile motion, circular motion, and Kepler's laws.

LINEAR ALGEBRA
Vector and matrix algebra, vector spaces, matrix decomposition, complex matrices, matrix inversion, Gaussian elimination, linear independence, matrix rank, determinants, linear transformations, symmetric and Hermitian matrices, orthogonal matrices, LU and QR factorisation, eigenvalues and eigenvectors, diagonalization, PCA, SVD, ARMA, and quadratic forms.

COMPLEX ANALYSIS
Cartesian and polar form, complex functions, complex polynomials and roots, complex differentiation, holomorphic functions, Cauchy-Reimann Equations, Euler's formula, complex line integrals, Cauchy's integral formula, complex power and Taylor series, Laurent series, poles and zeros, and residue integration.

FUNCTIONAL ANALYSIS
Cubic and quartic functions, logarithms, trigonometric functions, polynomials, rational functions, inverse functions, graphing functions, composition, quotient and product of functions, average value of a function, limits, limit laws, continuity, functions in nonlinear coordinates, convolution, function transforms (Laplace, Fourier, and Z), sequences and series, alternating series, comparison and integral test, ratio and root test, absolute convergence, power series, Taylor series, and Maclaurin series.

DIFFERENTIATION
Product and quotient rules, chain rule, indeterminate forms, l'hospitals rule, the mean value theorem, partial derivatives, directional derivatives, Lagrange multipliers, implicit differentiation.

INTEGRATION
Integration by parts, substitution, partial fractions, trigonometric integration, the fundamental theorem of calculus, line integrals, surface integrals, double and triple integrals, arc length, area, volume, work, integration in nonlinear coordinates, change of variables, Feynman's technique, and other integration techniques.

PROBABILITY
Experiments, outcomes, events, measures of spread, random variables, permutations, combinations, mean, variance, covariance, expected value, probability laws, law of large numbers, central limit theorem, Bayes' theorem, distributions (Binomial, Multinomial, Hypergeometric, Geometric, Poisson, and Normal), multivariate distributions, sampling, estimators, parameters, statistics, correlation, regression, confidence intervals, hypothesis testing, quality control, Markov chains, and Bayesian networks.

SOFTWARE ARCHITECTURE
Data types, OOP, control structures, unary and binary operators, loops, conditionals, functions, scope, the call stack, templates, recursion, iteration, arrays, vectors, lists, stacks, queues, trees, searching and sorting algorithms, pointers, classes and objects, interface vs implementation, constructors and destructors, private vs public members, proxy classes, operator overloading, static vs dynamic objects, lambda functions, inheritance, polymorphism, switch statements, data streams, reading-from and writing-to files, exception handling, strings, self-referential classes, type casting, prototype, singleton, state machine, game loops, update method, object pool, dirty flag, observer, model-view-controller, curiously recurring template pattern, double buffering, type object, data locality, and spatial partition.

DIGITAL ELECTRONICS
Finite state machines, Boolean algebra, logic gates, Karnaugh maps, encoding, latches, registers, decoders, PALs, PLAs, ROMs, multiplexers, RAM, ALUs, controllers, and buffers.

GRAPH THEORY
Big and little O complexity, types of graphs, shortest path algorithms, DFS, BFS, A-star, Prim, Dijkstra, greedy search, and heuristic search.

Tutoring Approach:

Mathematics is taught very badly at school and not much better at university. That's why it’s so important to find good maths teachers. These can be people at your school or college, authors of textbooks, online video presenters, or tutors. Personally, I've found the latter 3 options to be much better.

Each student has specific needs. I won’t know what these are until I meet a student and understand how they learn. But there are certain teaching mechanisms that are proven to be effective in most cases:
• Revising a student’s weekly content, to establish where they are struggling.
• Guiding a student though problems, to understand how they think.
• Reframing a topic, to make it more accessible from a student’s perspective.
• Illustrating a topic graphically, via software, short video, diagram, or sketch.

A good maths teacher makes things simpler, not the other way around. When someone intentionally complicates a subject, it only serves to elevate their status and the status of the subject.

Maths is about simplifying and slowing things down. It’s about dissecting a problem into its most basic components (or axioms), understanding each of these axioms separately, and then putting it all back together to reach a beautiful conclusion. Speed comes with repetition and practice.

Like a good coach training his players, I'm here to guide my students, not do the work for them. Its vital they apply themselves, practice in their own time, and hopefully build an interest in what they're studying. These 3 ingredients together with a good tutor is bound to result in success.

MY DOS AND DONTS

*** I offer an initial 1-hour free lesson per family (not per student).

*** I offer lessons online and in-person at my place of residence in Mornington, Victoria.

*** I offer lessons that are 1, 2, 3 or 4 hours long (no half-hour lessons).

*** I do not purchase textbooks, but (at my discretion) I may be able to acquire them via other means.

*** I do not purchase calculators, but (at my discretion) I may be able to access them online.