Introduction to Data Science
Foundations, Applications, and Mathematical Background
Dr. Ali Abubakar
Academic City University
January 16, 2026
Dr. Ali Abubakar (Academic City University) Introduction to Data Science January 16, 2026 1 / 15
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Introduction to Data Science
Foundations, Applications, and Mathematical Background
Dr. Ali Abubakar
Academic City University
January 16, 2026
Lecture Outline
(^1) Definition of Data Science
(^2) Applications of Data Science
(^3) Why Data Science?
(^4) Components of Data Science
(^5) Why Mathematical Foundations?
6 Requirements: Scientific Python
Data Science vs Related Fields
Statistics: inference, uncertainty, hypothesis testing Computer Science: algorithms, data structures, scalability Machine Learning: predictive models from data AI: intelligent decision systems
Key Idea
Data Science integrates all these to solve data-driven problems.
Applications of Data Science
Artificial Intelligence Image recognition Speech and language processing Recommendation systems Finance Risk modeling Fraud detection Algorithmic trading Healthcare: disease prediction, medical imaging Engineering: predictive maintenance, signal analysis Business: customer analytics, demand forecasting Government: policy analysis, population modeling
Core Components of Data Science
Data collection and preprocessing Exploratory data analysis (EDA) Mathematical modeling Machine learning algorithms Model evaluation and deployment
Why Mathematics in Data Science?
Fundamental Truth
Data Science is applied mathematics implemented on computers.
Models are mathematical functions Learning means optimization Uncertainty requires probability theory
Why Calculus?
Learning = minimizing a loss function Gradients guide parameter updates Backpropagation is calculus-based
θt+1 = θt − η∇L(θt )
Why Optimization?
Models are trained by solving optimization problems Convex and non-convex optimization Trade-off between accuracy and complexity
Goal
Find the best model parameters efficiently and reliably.
Scientific Python Stack
NumPy: numerical computing, linear algebra SciPy: optimization, statistics Pandas: data manipulation Matplotlib / Seaborn: visualization Scikit-learn: machine learning
Summary
Data Science integrates math, computing, and data Applications span AI, engineering, finance, healthcare Mathematics is the backbone Scientific Python is the main toolset
Next
We begin with mathematical foundations and hands-on Python.