From Equations to Intelligence: A Deep Dive into Data Science and AI

Lecturer

Dr Alina Donea, Monash University

Synopsis

From Equations to Intelligence: A Deep Dive into Data Science and AI is an intensive course designed to bridge mathematical foundations with practical applications in modern Artificial Intelligence. Spanning four weeks, it provides participants with a rigorous yet accessible pathway from the fundamentals of data science to the core mechanics of deep learning.

Week 1 introduces the landscape of Data Science, covering its impact, career opportunities, and essential tools such as data structures, representations, and visualization, with a focus on Python (intermediate level).

Week 2 consolidates the mathematical backbone of AI, revisiting advanced linear algebra, probability, and statistics, and introducing core techniques such as Singular Value Decomposition, PCA, and optimization algorithms. Neural networks are introduced alongside Python problem sets to strengthen applied understanding.

Week 3 dives deeper into the mathematics of machine learning models, explaining the principles behind convolutional neural networks, support vector machines, sequence models, and generative models. Practical coding sessions ensure theoretical concepts are tied to implementation.

Week 4 focuses on advanced aspects of deep learning, including feature selection, convex optimization, runtime considerations, and modern architectures such as Transformers.

Course Overview

Week 1: Data Science

  • Introduction to Data Science concept, The impact of data today , What jobs are on the market and how can you get hired
  • Data Structures, Representations, Mathematical Visualisation
  • Python material (Intermediate)

Week 2: Mathematics for AI

  • A short-long revision of advanced topics in Linear Algebra: vectors, matrices, eigenvalues, kernels, Probability & Statistics for AI
  • Singular Value Decomposition as a dimensionality reduction technique, Image Compression, Eigenfaces for Recognition, Principal Component Analysis (PCA)
  • Gradient descent and Stochastic gradient descent, optimization algorithms, Adaptive and coordinate-wise learning rate
  • Principles of machine learning, Neural Networks
  • Python material and Problem sets

Week 3: Breaking Down the Mathematics Behind ML Models 1: A Comprehensive Guide and Applications

  • Neural Networks Convolutional Neural Networks
  • Support Vector Machines
  • Sequence Models
  • Generative Models
  • Python and Questions

Week 4: Mathematics of Deep Learning 2: A Comprehensive Guide and Applications

  • Feature Selection and Generation
  • Runtime of Learning , Convex LEarning
  • Transformers

Prerequisites

• First- and second-year linear algebra (linear maps, kernel, image, etc)
• Probabilities second year, Calculus second year level.
• Basic coding experience is required. Pre-workshop materials will be provided, and completing the beginner Python module (on Moodle) before the school starts is compulsory.

Assessment

1. Assignments – 45%

  • 4 weekly small mathematics tasks
  • 4 Python/AI coding tasks

2. GitHub, Coding Beauty, Data Visualisation – 5%

  • Upload code, data, and create a webpage for your work

3. Team Leadership , Use of AI Tools – 15%

  • Help design and coordinate workshop tasks for peers
  • Apply ChatGPT or similar tools to solve mathematical problems in AI. demonstrate how AI tools like ChatGPT can be used in real-time to support mathematics and coding for AI applications. Reflection and Evaluation.

4. Final Project – 35% (Test online 5%, Project 30%)

  • A full end-to-end project showcasing your skills

Resources/pre-reading

Students are expected to bring their own laptops/devices to Summer School to complete this subject.

  • The coding part of the unit will be taught in the open source programming environment Python. To prepare for this material students should install python and do the pre-workshop materials provided on Moodle, and completing the beginner Python module (on Moodle) before the school starts is compulsory.
  • Tensor flow, Keras, Sci-kit libraries required

Not sure if you should sign up for this course?

Take this pre-enrolment QUIZ to self-evaluate and get a measure of the key foundational knowledge required. NOTE: this is a google drive link containing a Jupyter python notebook.

Dr Alina Donea, Monash University