Introduction to numerical analysis from Coursera

Numerical computations historically play a crucial role in natural sciences and engineering. These days however, it’s not only traditional «hard sciences»: whether you do digital humanities or biotechnology, whether you design novel materials or build artificial intelligence systems, virtually any quantitative work involves some amount of numerical computing . These days, you hardly ever implement the whole computation yourselves from scratch. We rely on libraries which package tried-and-tested, battle-hardened numerical primitives. It is vanishingly rare however that a library contains a single pre-packaged routine which does all what you need. Numerical computing involves assembling these building blocks into computational pipelines. This kind of work requires a general understanding of basic numerical methods, their strengths and weaknesses, their limitations and their failure modes. And this is exactly what this course is about. It is meant to be an introductory, foundational course in numerical analysis, with the focus on basic ideas. We will review and develop basic characteristics of numerical algorithms (convergence, approximation, stability, computational complexity and so on), and will illustrate them with several classic problems in numerical mathematics. You will also work on implementing abstract mathematical constructions into working prototypes of numerical code. Upon completion of this course, you will have an overview of the main ideas of numerical computing, and will have a solid foundation for reading up on and working with more advanced numerical needs of your specific subject area. As prerequisites for this course, we assume a basic command of college-level mathematics (linear algebra and calculus, mostly), and a basic level of programming proficiency. Do you have technical problems? Write to us: [email protected]

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Foundational review and development of basic numerical methods and algorithms

Introduces strengths, weaknesses, limitations, and failure modes of numerical approaches

Strengthens core skills for STEM and quantitative data work

Provides a solid overview of the main ideas of numerical computing

It is expected that students have basic college-level math and programming knowledge

Reviews summary

Strong numerical analysis introduction

This course provides a well-structured introduction to the fundamental principles of numerical analysis. Learners will appreciate opportunities to implement theoretical concepts in Python assignments. Classes will require significant mathematical background to fully participate in explanations and challenging assignments.

High quality video production.

"Dr. Evgeni Burovski explains the various topics very well..."

"The Jupyter notebooks were good..."

Appropriate for beginners.

"It's a great course for introduction to numerical analysis methods."

"This course is meant to be an introductory, foundational course in numerical analysis..."

Tough but worthwhile assignments.

"The course is challenging enough, but explanations are too pure."

"Pretty rigorous course, takes time to think and solve the assignments. Loved it."

Assignments strengthen understanding.

"...assignments really helped drill a lot of those abstract concepts home for me, so all in all it was a great learning experience."

"...Assignments are really good !"

Requires college-level math understanding.

"Overall a very good course for introducing students to numerical methods. The only thing I would wish for is that there were more exercises."

"And some exercises just jumped to topics that weren't fully covered in class, so I needed to read up from other sources."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Introduction to numerical analysis with these activities:

Review Calculus and Linear Algebra

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A quick review of these topics will help you refresh your memory and prepare for the course.

Browse courses on Calculus

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Go through your old notes or textbooks to review the basics of calculus and linear algebra.
Work through some practice problems to test your understanding.

Review Linear Algebra

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This course heavily utilizes linear algebra, so refreshing your skills will help you achieve better results

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Review the basics of linear algebra, including concepts such as vectors, matrices, and matrix operations.
Practice solving systems of linear equations using various methods.

Review Calculus

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A strong foundation in calculus will greatly benefit your performance in this course.

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Review the basics of calculus, including concepts such as limits, derivatives, and integrals.
Practice solving calculus problems, such as finding derivatives and integrals of various functions.

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Numerical Analysis

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Reading this book will provide you with a deeper understanding of the concepts covered in this course.

View Numerical Analysis on Amazon

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Read the textbook chapters that correspond to the topics covered in the course.
Solve the practice problems at the end of each chapter.

Online Tutorials on Numerical Methods

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These tutorials will provide you with additional practice and examples of numerical methods.

Browse courses on Numerical Methods

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Find online tutorials on numerical methods that cover the topics you are studying in the course.
Follow the tutorials and complete the exercises.

Practice Numerical Methods Problems

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Solving practice problems will help you develop your skills in numerical methods.

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Find practice problems on numerical methods that cover the topics you are studying in the course.
Solve the practice problems and check your answers against the provided solutions.

Numerical Recipes

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This classic book provides a comprehensive overview of numerical methods and is a valuable resource for further study.

View Numerical Recipes in C++ on Amazon

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Read the chapters of the book that correspond to the topics covered in the course.
Work through the exercises at the end of each chapter to test your understanding.

Create a Summary of Numerical Methods Concepts

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Creating a summary will help you solidify your understanding of the concepts covered in the course.

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Review the notes and materials from the course.
Identify the key concepts and ideas in each topic.
Write a summary of each concept, explaining it in your own words.

Career center

Learners who complete Introduction to numerical analysis will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists leverage large datasets to generate insights that support strategic decision-making and problem-solving. This course in numerical analysis provides a strong foundation in the mathematical concepts and algorithms used in data science. You will learn how to analyze data, build models, and draw conclusions from complex datasets, which are essential skills for success in this field.

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Financial Analyst

Financial Analysts use numerical methods to evaluate investments, make financial projections, and develop financial strategies. This course in numerical analysis will help you build a strong foundation in the mathematical techniques used in financial analysis, enabling you to make informed decisions and effectively manage financial risks.

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Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. This course in numerical analysis will provide you with the necessary mathematical background and computational skills to succeed in this highly competitive field.

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Software Engineer

Software Engineers design, develop, and maintain software systems. This course in numerical analysis will equip you with the mathematical and computational skills necessary to develop efficient and reliable software, particularly in areas that involve numerical computations, such as scientific computing or data analysis.

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Actuary

Actuaries use mathematical and statistical techniques to assess and manage financial risks. This course in numerical analysis will provide you with the necessary mathematical foundation to understand and apply actuarial models, enabling you to make informed decisions and effectively manage risks.

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Biostatistician

Biostatisticians use statistical methods to analyze biological and medical data. This course in numerical analysis will provide you with the necessary mathematical background and computational skills to develop and apply statistical models in biomedical research, enabling you to make informed conclusions and contribute to advancements in healthcare.

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Computational Scientist

Computational Scientists use mathematical and computational techniques to solve complex problems in science and engineering. This course in numerical analysis will provide you with the necessary mathematical and computational skills to develop and apply numerical models, enabling you to make advancements in scientific research and technological innovations.

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Data Engineer

Data Engineers design, build, and maintain data infrastructure and systems. This course in numerical analysis will provide you with the necessary mathematical and computational skills to develop and optimize data pipelines, enabling you to effectively manage and process large datasets.

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Machine Learning Engineer

Machine Learning Engineers develop and deploy machine learning models. This course in numerical analysis will provide you with the necessary mathematical and computational background to understand and apply numerical methods in machine learning, enabling you to develop and optimize machine learning models.

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Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to analyze and optimize business processes. This course in numerical analysis will provide you with the necessary mathematical foundation to understand and apply optimization models, enabling you to make informed decisions and improve operational efficiency.

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Physicist

Physicists use mathematical and computational techniques to study the fundamental laws of nature. This course in numerical analysis will provide you with the necessary mathematical and computational skills to develop and apply numerical models in physics, enabling you to make advancements in scientific research and technological innovations.

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Risk Manager

Risk Managers identify, assess, and manage risks. This course in numerical analysis will provide you with the necessary mathematical and computational skills to develop and apply risk models, enabling you to make informed decisions and effectively manage risks in various industries.

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Statistician

Statisticians use statistical methods to collect, analyze, and interpret data. This course in numerical analysis will provide you with the necessary mathematical and computational skills to develop and apply statistical models, enabling you to make informed conclusions and contribute to advancements in various fields.

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Teacher

Teachers educate and inspire students in various subjects. This course in numerical analysis may be useful for teachers who wish to enhance their understanding of mathematical concepts and computational techniques, enabling them to effectively teach these subjects to students.

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Economist

Economists use mathematical and statistical techniques to analyze economic data and make economic forecasts. This course in numerical analysis may be useful for economists who wish to enhance their understanding of mathematical models and computational methods used in economic analysis.

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