Math Every Data Scientist Needs
Why is Math Important in Data Science?
Data science is a fast-growing discipline. According to the American Statistical Association, the number of data science degrees granted by American universities grew tenfold between 2020 and 2022. This surge underscores the increasing recognition of data science’s pivotal role in various industries.
The Misconception: It’s All About Programming
A common misconception for students entering a data science program is that it’s all about programming in Python or R. But that couldn’t be further from the truth. You need a deep understanding of math and statistics to make sense of data and know whether an algorithm is appropriate for a given task. Cases where you can readily use an out-of-the-box function for real-world problems are few and far between.
The Crucial Role of Math in Data Science
A thorough understanding of math is crucial to student success in data science courses. Common topics data science majors need to master include algebra and functions, calculus, probability and statistics, linear algebra, and discrete math. Let’s delve into why these mathematical foundations are indispensable.
Key mathematical topics
First, a not-so-rhetorical question: What is data science, anyway? Think of the discipline as the entire process of working with a dataset and extracting meaningful insights from it. While no consensus curriculum yet exists, you’ll want to cover the following foundational topics in your classes:
Algebra and Functions
Algebraic equations and functions are essential for manipulating and transforming data, as well as describing relationships between features. Applications include:
- Data Wrangling: Standardization, normalization, and imputation.
- Activation Functions: ReLU, sigmoid, and tanh.
- Functions as Models: Linear regression and logistic regression.
Probability and Statistics
Probability and statistics provide tools for interpreting and analyzing data, which are critical steps in decision-making. Applications include:
- Descriptive Statistics: Mean, median, and mode.
- Data Visualization: Creating insightful graphs and charts.
- Predictive Modeling: Decision trees and hypothesis testing.
Calculus
Many machine learning algorithms involve optimizing a cost or loss function to improve model performance. Derivatives are used to find the minima of such functions. Applications include:
- Backpropagation: Essential for training neural networks.
- Gradient Descent: A method for optimizing algorithms.
- Regularization Techniques: L1 and L2 regularization.
Linear Algebra
Linear algebra provides a simpler way to represent large data sets and perform calculations using vectors and matrices. Applications include:
- Principal Component Analysis: Reducing dimensionality of data.
- Computer Vision: Filters and pooling in image processing.
Discrete Math
Advanced techniques in machine learning and artificial intelligence often require an understanding of formal logic and graph theory, which are commonly taught in discrete math courses. Applications include:
- Reinforcement Learning: Algorithms that learn from interactions.
- Natural Language Processing: Understanding and generating human language.
- Graph Neural Networks: Analyzing graph-structured data.
“A common misconception for students entering a data science program is that it’s all about programming in Python or R. But that couldn’t be further from the truth. You need a deep understanding of math and statistics to make sense of data and know whether an algorithm is appropriate for a given task. Cases where you can readily use an out-of-the-box function for real-world problems are few and far between.”
How zyBooks can help
While the amount of math required may seem overwhelming, mastering these key topics is both achievable and rewarding. It allows students to follow different data science and machine learning workflows from beginning to end, while keeping an eye on important assumptions to determine if an algorithm or model is the right fit for a particular application.
Relevant zyBooks
To ensure students can review relevant material, the following zyBooks can be combined with Data Science Foundations:
The interactive content in zyBooks simplifies concepts into manageable and easy-to-understand pieces for students. Additionally, the platform comes with built-in activity tracking and auto-grading features that allow both students and instructors to monitor progress and provide immediate and actionable feedback.
By integrating these resources, students can build a strong mathematical foundation, which is essential for excelling in the dynamic field of data science.
See related articles: How to teach Data Science – zyBooks Guide, Building student confidence in R, Computing Competencies for Data Science
