Master Advanced Mathematics for Data Science, Economics, Engineering,  AI and more.

Online tutoring for Linear Algebra, Multivariable Calculus and Differential Equations – by a PhD Mathematician.

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Welcome to UniMaths Academy

At UniMaths Academy, we believe that advanced mathematics is the foundation of innovation, technology, and scientific breakthroughs. Our goal is to equip engineers, scientists, and innovators with the mathematical tools they need to tackle complex challenges, optimize solutions, and drive progress across industries.

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About UniMaths Academy

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Led by Dr. Hannelie Brooks, a PhD mathematician, UniMaths Academy offers expert-led tutoring in Linear Algebra, Multivariable Calculus, Differential Equations, and other advanced mathematics topics.

Whether you’re a university student preparing for rigorous exams, a data scientist mastering optimization, or an engineer applying mathematical models in real-world applications, our structured learning programs provide clarity, depth, and practical insights.

Learn, Apply, Innovate

Mathematics for the future of technology and discovery.

Our Courses

Advanced Linear Algebra for Data Science, Machine Learning, and Engineering

Topics Covered:
  • Matrix operations and vector spaces
  • Eigenvalues, eigenvectors, and diagonalization
  • Singular Value Decomposition (SVD) and Principal Component Analysis (PCA)
  • Linear transformations and real-world applications
Who Should Take This Course?

For students in engineering, computer science, data science, and physics who want to build a rock-solid foundation in vector spaces, matrices, and linear transformations.

Learn the language of modern science, machine learning, and quantum theory.

Your learning, your pace – choose what works best for you!

At Advanced UniMath Academy, flexibility is key. Our structured courses are designed to fit your schedule while maximizing mastery of complex mathematical concepts.

Choose Your Ideal Learning Format:

  • 60-minute express sessions – Perfect for focused learning on specific topics.
  • 90-minute deep-dive lessons – Ideal for tackling complex theories and problem-solving strategies.
  • 120-minute intensive masterclasses – Designed for advanced learners who need in-depth coaching.

Convenient Scheduling: Choose from weekday, evening, and weekend sessions to fit your routine.

What’s Included in Every Session?

  • Expert-Led Teaching – Learn directly from an experienced mathematician.
  • LaTeX-Based Study Notes – Professionally formatted materials for deep
    comprehension.
  • Interactive Problem-Solving – Engage in live discussions, exercises, and
    applications.
  • Certification Upon Completion – Validate your mastery with an official
    UniMath Academy certificate.

Flexible bookings-structured for your success! Ready to start? Choose your session and book today!

Module 1: Foundations of Linear Algebra

  1. Vector Spaces & Subspaces
    • Basis, dimension, and linear independence.
    • Applications in computational mathematics.
  2. Matrix Operations
    • Matrix addition, multiplication, and inversion.
    • Special matrices: symmetric, diagonalizable, and orthogonal matrices.
  3. Linear Transformations
    • Geometric interpretations and real-world applications.

Module 2: Eigenvalues, Eigenvectors, and Diagonalization

  1. Eigenvalue Decomposition
    • Definition and importance in stability analysis.
    • Diagonalizing a matrix step-by-step.
  2. Applications
    • Markov chains, physics simulations, and quantum mechanics.

Module 3: Singular Value Decomposition (SVD)

  1. Understanding SVD
    • Matrix decomposition.
    • Interpreting singular values in feature reduction.
  2. Applications
    • Principal Component Analysis (PCA).
    • Noise reduction in images and data compression.

Module 4: Inner Products and Norms

  1. Inner Product Spaces
    • Gram-Schmidt Orthogonalization.
  2. Vector Norms & Distance Metrics
    • Frobenius and spectral norms.
  3. Applications
    • Optimization and machine learning loss functions.

Module 5: Advanced Matrix Factorization

  1. LU, QR, and Cholesky Factorization
    • Direct methods for solving linear systems.
  2. Applications
    • Scientific computing and numerical stability.
enrol now book a free consultation

Advanced Multivariable Calculus for Optimization & Applied Sciences

Topics Covered:
  • Partial derivatives and gradients
  • Vector calculus and integral theorems (Stokes, Gauss)
  • Constrained optimization (Lagrange multipliers)
  • Applications in finance, optimization, and engineering
Who Should Take This Course?

Perfect for STEM learners tackling problems in physics, engineering, and economics, where functions depend on more than one variable.

Gain the tools to explore 3D space, gradients, optimization, and vector fields.

Your learning, your pace – choose what works best for you!

At Advanced UniMath Academy, flexibility is key. Our structured courses are designed to fit your schedule while maximizing mastery of complex mathematical concepts.

Choose Your Ideal Learning Format:

  • 60-minute express sessions – Perfect for focused learning on specific topics.
  • 90-minute deep-dive lessons – Ideal for tackling complex theories and problem-solving strategies.
  • 120-minute intensive masterclasses – Designed for advanced learners who need in-depth coaching.

Convenient Scheduling: Choose from weekday, evening, and weekend sessions to fit your routine.

What’s Included in Every Session?

  • Expert-Led Teaching – Learn directly from an experienced mathematician.
  • LaTeX-Based Study Notes – Professionally formatted materials for deep
    comprehension.
  • Interactive Problem-Solving – Engage in live discussions, exercises, and
    applications.
  • Certification Upon Completion – Validate your mastery with an official
    UniMath Academy certificate.

Flexible bookings-structured for your success! Ready to start? Choose your session and book today!

Module 1: Fundamentals of Multivariable Calculus

  1. Partial Derivatives and the Gradient
    • Definition of partial derivatives.
    • The gradient vector and directional derivatives.
    • Applications in machine learning and optimization.
  2. Tangent Planes and Linear Approximations
    • Multivariable Taylor series expansion.
    • Application in error estimation and predictive modeling.
  3. Linear Transformations
    • Geometric interpretations and real-world applications.

Module 2: Vector Calculus and Integral Theorems

  1. Divergence, Curl, and Vector Fields
    • Physical interpretation of divergence and curl.
    • Applications in fluid dynamics and electromagnetism.
  2. Line and Surface Integrals
    • Green’s Theorem, Stokes’ Theorem, and Gauss’ Divergence Theorem.
    • Case studies in engineering and economic modeling.

Module 3: Constrained Optimization and Lagrange Multipliers

  1. Optimization in Higher Dimensions
    • Finding local extrema for multivariable functions.
    • Hessian matrix and convexity analysis.
  2. Lagrange Multipliers for Constrained Optimization
    • Applications in finance, economics, and Al model optimization.
    • Solving resource allocation problems.
enrol now book a free consultation

Advanced Differential Equations for Scientific and Computational Applications

Topics Covered:
  • Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs)
  • Fourier and Laplace transforms
  • Numerical methods (Finite Difference, Finite Element)
Who Should Take This Course?

Designed for learners in applied math, engineering, biology, and finance who need to model change and real-world dynamics over time.

Bring life to equations-whether you’re studying circuits, epidemics, or motion.

Your learning, your pace – choose what works best for you!

At Advanced UniMath Academy, flexibility is key. Our structured courses are designed to fit your schedule while maximizing mastery of complex mathematical concepts.

Choose Your Ideal Learning Format:

  • 60-minute express sessions – Perfect for focused learning on specific topics.
  • 90-minute deep-dive lessons – Ideal for tackling complex theories and problem-solving strategies.
  • 120-minute intensive masterclasses – Designed for advanced learners who need in-depth coaching.

Convenient Scheduling: Choose from weekday, evening, and weekend sessions to fit your routine.

What’s Included in Every Session?

  • Expert-Led Teaching – Learn directly from an experienced mathematician.
  • LaTeX-Based Study Notes – Professionally formatted materials for deep
    comprehension.
  • Interactive Problem-Solving – Engage in live discussions, exercises, and
    applications.
  • Certification Upon Completion – Validate your mastery with an official
    UniMath Academy certificate.

Flexible bookings-structured for your success! Ready to start? Choose your session and book today!

Module 1: Fundamentals of Differential Equations

  1. Classification of Differential Equations
    • ODES vs. PDES
    • Linear vs. Nonlinear equations
  2. First-Order Differential Equations
    • Separable equations
    • Exact and integrating factor methods
    • Applications in population dynamics
  3. Second-Order Differential Equations
    • Homogeneous and non-homogeneous cases
    • Method of undetermined coefficients
    • Real-world uses: mechanical vibrations, electrical circuits

Module 2: Partial Differential Equations (PDEs)

  1. Wave, Heat, and Laplace Equations
    • Boundary value problems
    • Fourier series solutions
    • Applications in signal processing and thermodynamics
  2. Numerical Methods for PDEs
    • Finite Difference and Finite Element Methods

Module 3: Fourier and Laplace Transforms in Differential Equations

  1. Transform Methods for Solving ODEs & PDEs
enrol now book a free consultation

At UniMaths Academy, we don’t just teach math – we unlock its power for real-world applications in data science, engineering, economics, and more.

Pricing Table in ZAR

Invest in world-class instruction, structured materials, and a transformative learning experience.

60 minutes

R600
Perfect for quick concept reviews or focused guidance.

90 minutes

R750
Perfect for deep topic exploration with guided practice

120 minutes

R900
Perfect for comprehensive sessions with extended support

Linear Algebra

R6,400
8 × 90-min sessions (4 wks)

Multivariable Calculus

R8,000
10 x 90-min sessions (5 wks)

Differential Equations

R9,600
12 × 90-min sessions (6 wks)

Full Course Bundle
Get all 3 courses (30 sessions) as a bundle: R21,000
(Save R3,000!)

Monthly Mentorship

R3,800
4 x 2-hour private sessions

Exam Bootcamp

R2,700
3 x 2-hour intensive prep sessions in 1 week

Tailored Researh Help

From R850/hour
Hourly coaching for thesis/academic projects

All sessions include LaTeX-based notes & personalized study insights.

Please contact us if you require training in any alternative maths module other than the courses listed above.

We can tailor a program to suit your needs.

enrol now

Join UniMaths in 3 Simple Steps

1

Choose a Course

Choose between a course in Linear Algebra, Calculus, Differential Equations or request a bespoke course based on your requirements.

2

Schedule a Free Consultation

Lets discuss your learning goals and create a structured plan tailored to your needs.

3

Start Learning

Begin your journey to mastering Linear Algebra, Calculus and beyond with expert guidance.

Ready to elevate your Mathematical skills?
Lets discuss your goals in a free consultation.

book a free consultation

Testimonials

Dr. Brooks is a patient, thorough and flexible teacher. Over the past few years, she has shown a keen interest in my learning style and has used this adjust her lessons so that it could be easier for me to grasp the given concepts. Additionally, Dr. Brooks is always prepared and her lessons are well structured. It is rare to find teachers of her caliber who are dedicated and motivated. Through her guidance and support I was able to understand concepts, which I found to be very challenging, further I was able to pass all my courses with good marks. I would never have been able to do so working on my own.

With the help of Dr. Brooks I have become a far more confident student not only in the mathematics courses, but in my other subjects too.

Thank you Dr. Brooks for the positive impact you have had on me as a student, and my studies.

Subjects:
Computational and Applied Mathematics II :Methods IIA (Ordinary Differential Equations) and Stochastic Calculus
Mathematics II: Basic Analysis, Linear Algebra, Multivariable Calculus, Advanced Analysis, Group Theory and Discrete Mathematics.
Mathematics Ill: Real Analysis, Group Theory, Number Theory, Complex Analysis, Leontief Systems and Cryptography.

Carolina C. Costa

Dr Brooks has had many years experience in tutoring university maths. She has always been approachable, has assisted and challenged me in understanding and resolving complex mathematical equations, and has an in depth knowledge and understanding of the challenges as well as what is required from students by the university faculties.

I found Dr Brooks to be very knowledgeable on the abovementioned subject matter and she played an integral role in assisting me to achieve a first class pass in both my years of study.

I have thoroughly enjoyed and more importantly grown under her tutelage and would highly recommend her services.

Subjects:
Major Maths 1: Calculus and Algebra
Major Maths 2: Linear Algebra, Multi-variable Calculus, Abstract Maths, Differential Equations and Introduction to real analysis

Elia Roussos 

As an undegraduate engineering student attending the University of the Witwatersrand, f had the pleasure of knowing Dr. Hannalie Brooks for three years. It was through her invaluable uition lessons that I was able to pass my subjects. She creates her own unique styles of learning that the student can casily grasp, and is very patient and motivating until the student understands a concept. The lessons are very engaging, and it is through this interaction that the student is able to truly understand a concept.

Dr. Brooks is easy-going and approachable. Her dedication and passion for mathematics is unrivalled. She has a very responsible attitude towards her work and the interests of her students. I recall that there were a few occasions when I was preparing for a test or exam where I required guidance outside of normal office hours, and she was more than willing to provide help.

I can truthfully say that I passed the courses only because of Dr. Brooks. She played a huge role in my pursuit of knowledge and I cannot thank her enough. It is for these reasons that I strongly recommend Dr Hannalie Brooks, without reservations.

Subjects:
Engineering Mathematics 1: Algebra and Calculus
Engineering Mathematics 2: Algebra and Calculus 
Engineering Mathematics 3: Laplace Transforms And Complex Variable Integration Techniques
Engineering Statistics

Alan Chen

On behalf of my son and myself I find that Dr. H Brooks to be an outstanding and flexible teacher. In the past couple of years she has shown a keen interest in Uzair’s learning styles and has used his learning styles to adjust her lessons which are always well structured. It is rare to find teachers of her caliber who are dedicated and motivated. I recognized this spirit when my son was in grade 11 in 2012. Her support and dedication not only helped him achieve the fantastic grades in his report card but also helped him to understand and grasp concepts which at first was challenging for him. 

Uzair has become a confident student as whole and this has been proven every single year when he continues to meet and actually go above grade level in his grades. Thank you Dr. H. Brooks for the positive impact you have had on my son in the past couple of years.

Subjects:
Advanced Programme Maths (Grade 11 and Grade 12)
Major Maths 1: Agebra and Calculus
Major Maths 2: Basic Analysis, Linear Algebra, Multivariable Calculus, Advanced Analysis, Abstract Algebra and Statistics.
Major Maths 3: Real Analysis, Group Theory, Number Theory
Complex Analysis, Leontief Systems and Cryptography

Mrs. Munira Moolla

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