Mathematical modeling skills will provide you with an edge over your peers when working in the data management sector. This skill is highly relevant to multiple job roles. Let’s discuss how mathematical modeling can help your career.
This comprehensive guide includes everything you need to know about mathematical modeling. You’ll understand what mathematical modeling entails as well as resources like classes and programs to help you learn the craft.
What Is Mathematical Modeling?
Mathematical modeling translates real-world problems into mathematics. Your models can help people visualize data and see issues in a new way.
Mathematical models can represent just about everything by utilizing equations, graphs, and other tools. This skill can be applied across several industries. Sectors that use mathematical modeling include finance, computer science, data analysis, genetic science, economic research, forecasting, and many more.
Wherever there is a practical problem with dependent and independent variables, then you can create an illuminating mathematical model.
What Is Mathematical Modeling Used For?
Mathematical modeling is applied across various areas to study and evaluate solutions, establish trends, and accurately analyze changes in a system. Some of the popular and wide-spread usages of mathematical modeling are listed below.
- Understanding a system’s behavior. Modeling allows you to evaluate a system both as a whole and in terms of individual variables.
- Quantitative hypothesis evaluation. Mathematical models can help check if a hypothesis is correct or if a researcher should return to their drawing board.
- Forecasting trends in a system. This tool also helps study patterns and predict how a system will behave.
- Relative comparison. Modeling helps you analyze problems concerning more than one factor or variable. This is needed to describe complex, real-life issues.
- Universal implementation. This field can help in disciplines like economics, biology, engineering, and many more.
- Risk analysis. The tool of mathematical modeling can help predict how events could positively or negatively affect a system.
Types of Mathematical Modeling
Linear Mathematical Modeling
This type of model shows linear trends. The graph of a linear model is always a straight line. A linear model consists of the rate of change, an initial value, and different data points along the y-axis and x-axis. This model is especially good at predictions.
Dynamic Mathematical Modeling
The dynamic mathematical modeling is used to account for variations in a system’s state. These models are used to anticipate interactions between multiple elements of a system over time.
Dynamic models are mostly represented by differential equations. They are typically used in dynamic behavior or trend analysis.
Implicit Mathematical Modeling
The implicit model is a mathematical representation across a volume. It has an infinitely-fine resolution and is considered a breakthrough in geographic modeling. This model has saved researchers much time in creating physical surfaces.
Continuous Mathematical Modeling
Continuous modeling is used on a continuous set of data. These models also use differential equations. A continuous model can represent a variable like fluid inside a system or temperature. The modeler makes assumptions as to what influences their data. They also create equations to fit their assumptions and then verify their hypothesis using tests.
Learning Mathematical Modeling
Learning basic concepts of mathematical modeling requires a keen interest, but it can be extremely enjoyable. Don’t be concerned about whether you’re learning through courses or books. All you need is some curiosity and a desire to explore and implement what you’re learning.
How Long Does It Take to Learn Mathematical Modeling?
Mathematical modeling can be learned in two ways. First, you can enroll in a bachelor’s degree program, which takes around three years to complete. Or you can opt for a master’s degree program which takes one to two years to finish.
However, there are multiple independent courses to help you understand mathematical modeling. You can master the fundamentals of this field in less than a week through an online course or internship program.
How to Learn Mathematical Modeling: Step-By-Step
We have compiled an in-depth guide for you to learn mathematical modeling, from the best free online courses to academic programs offered by top universities.
First, let’s break down your journey into five basic steps.
- Select an online course or training program. First, figure out what is better suited for you. Should you go the online route or attend a conventional training program? If you’re comfortable attending online classes, this is a great and flexible option.
- Get yourself enrolled. If you’ve decided to start your career in mathematical modeling, don’t waste time. Get yourself enrolled in an online course or training program and start preparing.
- Learn to code. Programming languages help a lot when building mathematical models. You should understand object-oriented programming and data structures. Later in this article, we’ll list online courses where you can learn coding.
- Increase your knowledge by reading books. Reading about this topic will give you some extra advantages. We have recommended some of the best books below to continue your learning.
- Learn calculus and its applications. Calculus is the medium of mathematical modeling. You should have a basic understanding of calculus and its applications in probability and differential equations. This will let you grasp key concepts more efficiently.
The Best Mathematical Modeling Courses and Training
If you’re looking for a degree, then check out some of these great courses we have compiled.
In-person Mathematical Modeling Classes
Listed below are the top on-campus bachelor’s degree and master’s degree programs. Enroll in one to pursue a professional career in mathematical modeling from a highly-reputable institution.
Deakin University
- Course: Bachelor of Science in Mathematical Modeling
- Length: 3 Years
- Prerequisites: None
- Cost: $37,000
This degree program offered by Deakin University will teach you through practical education. Classes are in modern laboratories, you will complete a community-science project, and you’ll have the opportunity for an industry-based placement exam.
You’ll develop robust and critical knowledge at Deakin that will increase your skills in analysis, logic, and problem-solving.
University of Oxford
- Course: Mathematical Modeling And Scientific Computing MSC
- Length: 1 year
- Prerequisites: Bachelor’s degree in a compatible disciple
- Cost: $31,411
This one-year master’s degree program introduces you to applied mathematics for a wide variety of science disciplines. The emphasis here is on problem formulation, analysis, mathematical solution techniques, and the computation of useful results.
Moreover, the degree is offered by one of the most reputable institutions in the world.
Best Online Mathematical Modeling Classes
There are many courses to learn about mathematical modeling online. But choosing the most suitable can be confusing. We have listed some of the most highly-recommended online courses and training programs below to help you out.
Coursera
- Course: Master Of Data Science
- Length: 2 years
- Prerequisites: Bachelor’s degree in a compatible disciple
- Cost: $8,901-$17,802
This master’s degree is designed for students regardless of prior technical skills. Its well-crafted curriculum was ranked first in Forbes’ “Universities for the Future Elite” list. The program will help you learn through applied projects with guidance from expert faculty.
edX
- Course: Mathematical Modeling Basics
- Length: 9 weeks
- Prerequisites: None
- Cost: $50
This course will give you an introduction to modeling. The instruction includes how to evaluate a problem, translate it into a mathematical model, calculate a solution, and verify your results. You’ll also learn to implement Euler’s Method in Python and how to publish your findings using LaTeX.
This course is extremely beneficial for students from engineering and mathematical or science disciplines. It’s highly recommended if you aim to use mathematical modeling to solve real-world problems.
Best Free Mathematical Modeling Courses
Below are some of the best free online certifications to help you polish your understanding of mathematical modeling. They teach you key concepts using relevant, real-world examples.
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National Programme on Technology Enhanced Learning
- Course name: Introduction to Mathematical Modeling
- Length: 4 weeks
- Prerequisites: None
- Cost: Free
This comprehensive online course is provided by one of the top tech institutes in the world. You’ll learn all about matrix algebra and linear models here. These models are widely used in many different fields.
You’ll also learn how to calculate statistical inference and use the R programming language to carry out matrix operations. This course is extremely fruitful for anyone with some basic knowledge of calculus and modeling.
Coursera
- Course name: Precalculus Through Data and Modeling Specialization
- Time: 4 months
- Prerequisites: None
- Cost: Free
This course gives an introduction to mathematical modeling. It helps you use mathematics to model, understand, and interpret the world around us. The course focuses on functions and their properties as well as data processing applications.
This course is for all levels and not just those interested in mathematics. If you like natural sciences, computer science, or human psychology, you’ll also benefit from this course.
FutureLearn
- Course name: Big Data: Mathematical Modeling
- Length: 3 weeks
- Prerequisites: None
- Cost: Free
This course gives you an introduction to key mathematical concepts in big data analytics like principal component analysis (PCA) and singular value decomposition. It will enable you to identify data application fields and work with big data effectively. In this course, you will be exploring real-world, big-data frameworks.
Books are a great way to refine your knowledge. There are several books you can refer to, but how do you know which ones are worth your time and money? To help you out, we have listed below the best books about mathematical modeling.
Best Mathematical Modeling Books
Mathematical Modeling: A Case Studies Approach, C. Sean Bohun
This book is great for advanced undergraduates. Each chapter ends with a collection of activities and suggestions for class assignments. Individual lessons are comprehensive and interesting, as when you learn about the predator-prey model.
Mathematical Modeling Techniques, Rutherford Aris
This textbook by Rutherford Aris is elegantly written and will help you learn mathematical modeling. It is engaging and explains techniques relevant to modeling in an elaborate yet simple way. The author has devised helpful rules for creating models to evaluate mathematical issues.
Mathematical Modeling And Simulation: Introduction For Scientists And Engineers, Kai Velten
This book is a concise and clear introduction to mathematical modeling. Anyone with a basic knowledge of calculus and linear algebra will love his text. The writing is clear and caters to both undergraduates and professionals.
It also allows readers to set up basic mathematical models on their own and view their findings critically. Throughout the book, you will develop a foundation for mathematical modeling and calculus.
Mathematical Modeling With Excel, Brian Albright
This book will help you develop models and interpret them using Microsoft Office Excel as a tool. The techniques and concepts in this text are updated and relevant to industry requirements. It presents a range of methods used to formulate and analyze mathematical models in a very student-friendly language.
Best Online Mathematical Modeling Resources
Here we have additional resources to help you in your quest to learn more about mathematical modeling. Listed are some free online resources like e-books and Youtube tutorials that will help you strengthen your understanding of key concepts.
Youtube.com
YouTube has become one of the best learning platforms around. It offers a number of teachers to choose from, each with a different approach. Check out channels like ‘Dr. Maths‘ and ‘Jacob Bishop‘ to brush up on mathematical modeling.
Math.Utah.Edu
This website by the University of Utah offers study material on a range of topics. It also offers one of the best free e-books on mathematical modeling.
Should You Study Mathematical Modeling?
Mathematical modeling plays a crucial role in many fields. It is especially helpful for businesses in today’s data-driven marketplace. The practical applications of modeling can be found in manufacturing, analytics and forecasting, finance and investment management, and insurance markets.
Mathematical modeling is an extremely versatile concept. Those that know their math fundamentals can always dream up new applications for their talent. And they will always be in demand. According to payscale.com the average annual salary for a person in this field is about $91,643.
Pursuing mathematical modeling as a full-time degree or gaining additional certifications in this area would be highly advantageous for anyone.
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