Machine learning and data science are emerging as popular fields of study from the career perspective. They set you up for a secure and lucrative career full of growth opportunities down the years. Once you get into the field, learning and growth never seem to end. You have excellent job prospects in diverse fields, and the income potential is also high. However, a lot of hard work, commitment, and dedication go into preparing yourself for a career in machine learning.

Much depends on the choice of the right subjects right from the beginning, and mathematics is the best place to start. If you are a math lover, you definitely have a bright scope with machine learning. Several core concepts of Maths and Statistics play a significant role in designing machine learning models. Before you pick the concepts you need to master, it makes sense to validate the use of mathematics for ML in the first place. After all, developing expertise in math requires a lot of effort, and you must have valid reasons for investing in it.

Table of Contents

## Why mathematics for machine learning?

Machine learning is all about mathematics as it helps create algorithms that learn from data and make accurate predictions. Hence, it is vital to understand the mathematical concepts that operate behind any central ML algorithm. Here are some reasons why you must choose it as a subject if you are serious about a career in this field.

- When you compare and choose machine learning algorithms, you need to consider accuracy, model complexity, training time, number of features, and number of parameters.
- Mathematics is the basis of selecting parameter values and validation methods.
- It helps in determining the correct uncertainty and confidence interval.
- A good understanding of the Bias-Variance tradeoff enables you to pick underfitting and overfitting issues that often occur when executing ML programs.

Clearly, you cannot choose algorithms and build models without a sound knowledge of mathematical concepts. But some concepts are more valuable than others when it comes to data science and machine learning. You can simply focus on these rather than spending time on the ones you will probably never use as a part of work. It makes sense to know these concepts to take a more granular approach to machine learning. Let us list the one you need to master to become an ML expert.

## Calculus

Mastering calculus gives you a good start if you want to step into the world of machine learning. Begin with learning and understanding the principles of calculus. You also need to comprehend the practical applications of ML through calculus while building models. The essential topics that help with data science include Differential and Integral Calculus, Directional Gradients, Partial Derivatives, and Vector-Values Functions. Algorithm training requires a strong understanding of multivariate calculus. You will need to learn and implement concepts such as divergence, curvature, derivatives, and quadratic approximations. While the sheer number of calculus concepts you have to know sounds overwhelming, you can catch up easily with only a few days of constructive learning.

## Probability Theory

When you work as a machine learning professional, you will come across predictive modeling projects more than once. Strong knowledge of probability theory makes things a lot easier with these projects. ML is basically about creating prediction models from raw data, so you will often have faulty or incomplete information to start with. You have to deal with uncertainty, which is often daunting for newbies. The proper probability tools get you on the right track as they help with the estimation of the solution to the problem. You can use probability concepts for hypothesis testing and distributions such as the Gaussian distribution.

## Linear Algebra

Another mathematical concept you cannot miss out on is linear algebra. Linear equations are the basis of the development of central machine learning algorithms. They help with the evaluation and observation of data collections. You will need to use linear algebra in algorithms in regularization, loss functions, covariance matrices, Matrix Operations, Singular Value Decomposition (SVD), and support vector machine classification. Further, you can apply it in learning algorithms such as linear regression. Linear algebra also finds use in neural networks, making it one of the key concepts of data science and machine learning.

## Discrete Mathematics

Discrete mathematics involves the study of non-continuous numbers, mainly integers. Many machine learning applications require the use of discrete numbers, so you need to have an in-depth understanding of this concept. A majority of AI structures are discrete. For example, a neural network has nodes and interconnections in an integer number. So the mathematics you use to develop a neural network should include a discrete element. The knowledge of only the fundamentals of discrete math is enough for machine learning. But you will have to dig deeper if you plan to work with relational domains, structured prediction, graphical models, and combinatorial problems.

## Descriptive Statistics

Another concept that every data scientist must understand is descriptive statistics. It builds a strong foundation for machine learning when you work with classifications such as logistic regression, discrimination analysis, distributions, and hypothesis testing. Statistics is the main element of mathematics for machine learning. You will need to master the fundamental concepts such as Axioms, Combinatorics, Bayesâ€™ Theorem, Random Variables, Variance and Expectation, and Joint Distributions. It is best to start early and gain an in-depth understanding of these subjects and topics.

## How to take your pick in concepts?

While a machine learning professional should have expertise in all these concepts, there are some simple guidelines to take your pick if you want to be more specific. It depends on the specialty you want to focus on while exploring career options in the field. Let us explain the details:

**Application-heavy positions** – When you start at an entry-level role in application-heavy positions, you will have to use out-of-the-box ML implementations. Thankfully, you need not reinvent the wheel, as most programming languages have robust libraries. Still, a basic understanding of linear algebra and multivariable calculus puts you in a good place. As you grow in the role, you will have to build custom implementations at some point. At this stage, you will have to extend your expertise to other concepts.

**R&D-heavy positions** – Professionals who plan to explore the research and development side of machine learning have to be more original in their approach. For example, you will have to translate algorithms from research papers into working code or study enhancements based on unique challenges. It means you will often need to implement algorithms from scratch. You will require more than just a basic understanding of concepts for such roles. Rather, a strong grip over all the five ML concepts is essential to building a successful career.

Machine learning is like a building that stands on the foundation of mathematical prerequisites. You cannot expect to create a strong building without a stable foundation. But it is wise to pick the right concepts and focus on them rather than be a jack of all trades. Mastering the aforementioned concepts gives you an excellent start with machine learning. While it may take some effort to ramp up your skills in these concepts, it is worthwhile to get a good start with your ML career and capitalize on it.