Mathematics has been an inescapable part of most disciplines in science and the same goes for data science. Almost all scopes of data science revolve around mathematics. It is also required that you have the basic knowledge in other fields such as programming, basic SQL query, analytical skills, etc. But mathematics stands par and requires understanding and work to design and analyze the data you work with.
Mathematical knowledge is required for each person irrespective of the field you come from as data science involves significantly different mathematics that are different from numeral calculations only.
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While other jobs may involve a lot of data, they only work on for a certain delivery and move and not entirely base on it. Similarly, it goes with data science, it is more about the science and not just the data. The scientific process involves, modeling a process from the underlying dynamics, building a hypothesis, estimating the quality of data, working around predictions by the data, identifying information. analyzing the model, understanding the math, and abstract behind it.
Data science is more diverse than any particular stream of work. It could deal with social behavior analysis and at the same time, demand for diagnosis of cancer with data science can be called. This possibly can include various segments of Mathematics like objects, functions, statistics, and lots more.
Here’s all you need to learn to ace the game
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Functions, Variables, Equations, Graphs
This is the basics one learns at school. You can easily brush up your knowledge in the following to help yourself:
Logs, exponents, polynomial functions, rational numbers, geometry, trigonometry, real and complex numbers, series, sums, inequalities, graphs, and Cartesian products.
You will come across scenarios where you have to perform a search in the piles of data. In this case, the binary search comes handy and to ace it you need an understanding of most of the concepts mentioned above.
Statistics and probability are an essential part of the learning. When you cover machine learning you will relate to statistics more. You can focus on Data summaries and descriptive statistics, central tendency, variance, covariance, correlation, Probability and distribution functions, Sampling, measurement, error, random number generation, Hypothesis testing, A/B testing, confidence intervals, p-values, ANOVA, t-test, Linear regression, regularization.
Since this is an essential topic that works in data science. Putting your skills on the interview table will be a great help.
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This is required for understanding how basic algorithms work with machine learning. Basic properties of matrix and vectors, Inner and outer products, matrix multiplication rule and various algorithms, matrix inverse, Special matrices, Matrix factorization concept/LU decomposition, Gaussian/Gauss-Jordan elimination, solving Ax=b linear system of equation, Vector space, basis, span, orthogonality, orthonormality, linear least square, Eigenvalues, eigenvectors, diagonalization, and singular value decomposition are the essential topics you should look into.
Neural network algorithms use linear algebra for network structuring and learning operations. You can use your knowledge in the singular value decomposition to create a compact dimension representation of your data set with comparatively fewer parameters.
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This is a quite complicated part of Mathematics and most of you must have disliked it in college. However, it is an essential part when it comes to data science and machine learning. Many simple-looking solutions may involve calculus to get to it. You might focus on learning Functions of a single variable, limit, continuity, differentiability, Maxima and minima, Product and chain rule, Mean value theorems, indeterminate forms, L’Hospital’s rule, Taylor’s series, infinite series summation/integration concepts, Fundamental and mean value-theorems of integral calculus, evaluation of definite and improper integrals, Beta and gamma functions, Functions of multiple variables, limit, continuity, partial derivatives, Basics of ordinary and partial differential equations.
For a logistic regression algorithm, a method called gradient descent is used and in order to understand the flow properly, you need to have an understanding of calculus to a level.
This part of mathematics isn’t as used as the few discussed earlier. However, certain modern techniques are using a computational system that involves discrete maths as the core. Brushing your skills in discrete math will be like working with algorithms and data structures. You may focus on Sets, subsets, power sets, Counting functions, combinatorics, countability, Basic proof techniques, Basics of inductive, deductive, and propositional logic, Basic data structures, Graph properties, Recurrence relations and equations, Growth of functions and O(n) notation concept.
When you are with social network analysis, the properties of a graph and fast algorithm will be in use to search and traverse the network. Also, the understanding of time and space complexity will be essential in such cases to conclude.
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Optimization and Operation Research topics
A basic understanding of this area will help a lot in the field of machine learning. Virtually every machine learning program deals with minimizing the data with error estimation subject to various parameters, which is simply optimizations. Focusing on basics of optimization, Maxima, minima, convex function, global solution, how to formulate a problem, Linear programming, simplex algorithm, Integer programming, Constraint programming, knapsack problem, Randomized optimization techniques: hill-climbing, simulated annealing, and genetic algorithms will help you go a long way.
This will come in handy when you have to deal with logistic regression problems. The concept of convexity in optimization will help you achieve the same. Along with this, you will get to understand why approximate solutions are pretty much the solutions in machine learning programming.
When you read through it, it might look like a lot and burying but these are probably things you have already learned in school, high school, and college. Just brushing up the concepts will help you more than you can think of. With the understanding of these concepts, you will be able to analyze your data much easier and find what’s under the table with your daily analysis and machine learning projects. This will take you ahead in your own journey towards being a data scientist.