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Mathematical Methods for Data Analysis

Mathematics has been playing an important role in data analysis from the very beginning; for example, Fourier analysis is one of the main tools in the analysis of image and signal data. This course is to introduce some mathematical methods for data analysis. It will cover mathematical formulations and computational methods to exploit specific structures contained in the data. Some special machine learning algorithms are introduced in case studies.

What you'll learn

Vector spaces, metrics and convergence
Case study: Clustering, k-means, k-medians
Inner product, Hilbert space
Case study: Kernel trick, kernel k-means; metrics learning
Linear functions and differentiation
Case study: Regression and classification; optimality and gradient descent

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What's inside

Learning objectives

Vector spaces, metrics and convergence
Case study: clustering, k-means, k-medians
Inner product, hilbert space

Case study: kernel trick, kernel k-means; metrics learning
Linear functions and differentiation
Case study: regression and classification; optimality and gradient descent

Vector spaces, metrics and convergence
Case study: clustering, k-means, k-medians
Inner product, hilbert space
Case study: kernel trick, kernel k-means; metrics learning
Linear functions and differentiation
Case study: regression and classification; optimality and gradient descent

Syllabus

Chapter 1: Introduction to mathematical analysis tools for data analysis

Chapter 2: Vector spaces, metics and convergence

Chapter 3: Inner product, Hilber space

Chapter 4: Linear functions and differentiation

Chapter 5: Linear transformations and higher order differentations

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Introduces essential mathematical tools for data analysis, including vector spaces and linear transformations, providing a strong basis for further learning in the field

Employs case studies to illustrate the practical applications of mathematical concepts in data analysis, such as clustering and regression

Taught by Jianfeng CAI, a respected instructor recognized for their contributions to data analysis and machine learning

Suitable for learners with a background in linear algebra and calculus, making it accessible to those with a foundation in these subjects

Helps learners develop a comprehensive understanding of mathematical methods used in data analysis, equipping them for more advanced study or professional practice

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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 Mathematical Methods for Data Analysis with these activities:

Organize your course materials regularly

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Ensuring your materials are organized, will minimize distractions while maximizing engagement with the course materials.

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Review your notes, assignments, quizzes, and exams.
Organize them in a logical way that makes sense to you.

Complete the MIT OpenCourseWare tutorial on linear functions and differentiation

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Build a stronger foundation in linear functions and differentiation by completing an MIT tutorial. These topics form the basis of much of the mathematics you will be using in this course and beyond.

Browse courses on Linear Functions

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Go to the MIT OpenCourseWare website and find the tutorial on linear functions and differentiation.
Complete the tutorial at your own pace, watching the videos and completing the exercises.

Vector space practice problems

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Practice working with vector spaces. Vector spaces are the core of much of what is done in linear algebra. This practice will pave the way for later successes.

Browse courses on Vector Spaces

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Work through the exercises in the textbook on vector spaces.
Find additional practice problems online or in other textbooks.

Four other activities

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Join a study group to discuss the course material

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Engage in peer learning to build a collaborative environment in the course.

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Find a group of classmates who are also taking the course.
Meet regularly to discuss the course material, work on assignments together, and quiz each other.

Answer questions in the course discussion forum

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Aid in fostering a positive and supportive learning environment.

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Monitor the course discussion forum regularly
Answer questions from other students to the best of your ability.

Create a poster on the applications of inner product spaces

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Demonstrate your understanding of the applications of inner product spaces.

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Research the applications of inner product spaces in different fields such as physics, engineering, and computer science.
Choose a specific application and explain how inner product spaces are used in that context.
Design and create a poster that visually presents your findings.

Build a machine learning model using the kernel trick

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Deepen your understanding of the kernel trick and its applications in machine learning.

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Learn about the kernel trick and how it is used in machine learning.
Choose a dataset and build a machine learning model using the kernel trick.
Evaluate the performance of your model and write a report on your findings.

Career center

Learners who complete Mathematical Methods for Data Analysis will develop knowledge and skills that may be useful to these careers:

Data Scientist

A Data Scientist uses their Mathematics and Statistics background to work on extracting insights and information from complex data. They use various techniques, including machine learning, artificial intelligence, and data mining, to solve problems. This course on Mathematical Methods for Data Analysis would be of great help to aspiring Data Scientists, as it provides a solid foundation in the mathematical concepts and techniques used in the field. The course covers topics such as vector spaces, metrics and convergence, inner product, Hilbert space, linear functions and differentiation, which are all essential for understanding and applying machine learning algorithms.

See salaries and explore the career path for Data Scientist

Machine Learning Engineer

Machine Learning Engineers are experts in building, deploying, and maintaining machine learning models. They work closely with Data Scientists to turn machine learning models into real-world applications. This course on Mathematical Methods for Data Analysis would be beneficial for Machine Learning Engineers, as it provides a strong foundation in the mathematical concepts underlying machine learning algorithms. The course covers topics such as vector spaces, metrics and convergence, inner product, Hilbert space, linear functions and differentiation, which are essential for understanding and applying machine learning techniques.

See salaries and explore the career path for Machine Learning Engineer

Data Analyst

Data Analysts use their skills in data analysis to help businesses make better decisions. They collect, clean, and analyze data, and then use that data to identify trends and patterns. This course on Mathematical Methods for Data Analysis would be helpful for aspiring Data Analysts, as it provides a solid foundation in the mathematical techniques used in data analysis. The course covers topics such as vector spaces, metrics and convergence, inner product, Hilbert space, linear functions and differentiation, which are all essential for understanding and applying data analysis techniques.

See salaries and explore the career path for Data Analyst

Business Analyst

Business Analysts use their analytical skills to help businesses improve their operations. They identify and solve problems, and develop recommendations for improvement. This course on Mathematical Methods for Data Analysis would be beneficial for Business Analysts, as it provides a strong foundation in the mathematical techniques used in data analysis. The course covers topics such as vector spaces, metrics and convergence, inner product, Hilbert space, linear functions and differentiation, which are essential for understanding and applying data analysis techniques.

See salaries and explore the career path for Business Analyst

Statistician

Statisticians use their skills in mathematics and statistics to collect, analyze, and interpret data. They work in a variety of fields, including healthcare, finance, and research. This course on Mathematical Methods for Data Analysis would be helpful for aspiring Statisticians, as it provides a solid foundation in the mathematical concepts and techniques used in statistics. The course covers topics such as vector spaces, metrics and convergence, inner product, Hilbert space, linear functions and differentiation, which are all essential for understanding and applying statistical techniques.

See salaries and explore the career path for Statistician

Software Engineer

Software Engineers design, develop, and maintain software applications. They work in a variety of industries, including technology, finance, and healthcare. This course on Mathematical Methods for Data Analysis may be helpful for Software Engineers who want to work in data-intensive fields, as it provides a foundation in the mathematical concepts and techniques used in data analysis.

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Quantitative Analyst

Quantitative Analysts use their skills in mathematics and statistics to analyze financial data and make investment decisions. They work in a variety of financial institutions, including investment banks, hedge funds, and asset management companies. This course on Mathematical Methods for Data Analysis may be helpful for aspiring Quantitative Analysts, as it provides a foundation in the mathematical concepts and techniques used in financial data analysis.

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Actuary

Actuaries use their skills in mathematics and statistics to assess risk and uncertainty. They work in a variety of industries, including insurance, finance, and consulting. This course on Mathematical Methods for Data Analysis may be helpful for aspiring Actuaries, as it provides a foundation in the mathematical concepts and techniques used in risk assessment.

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Operations Research Analyst

Operations Research Analysts use their skills in mathematics and statistics to solve problems in a variety of industries, including manufacturing, logistics, and healthcare. This course on Mathematical Methods for Data Analysis may be helpful for aspiring Operations Research Analysts, as it provides a foundation in the mathematical concepts and techniques used in operations research.

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Market Researcher

Market Researchers use their skills in mathematics and statistics to collect and analyze data about consumer behavior. They work in a variety of industries, including marketing, advertising, and consulting. This course on Mathematical Methods for Data Analysis may be helpful for aspiring Market Researchers, as it provides a foundation in the mathematical concepts and techniques used in market research.

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Financial Analyst

Financial Analysts use their skills in mathematics and statistics to analyze financial data and make investment decisions. They work in a variety of financial institutions, including banks, investment firms, and insurance companies. This course on Mathematical Methods for Data Analysis may be helpful for aspiring Financial Analysts, as it provides a foundation in the mathematical concepts and techniques used in financial analysis.

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Economist

Economists use their skills in mathematics and statistics to analyze economic data and make economic forecasts. They work in a variety of settings, including government agencies, research institutions, and private companies. This course on Mathematical Methods for Data Analysis may be helpful for aspiring Economists, as it provides a foundation in the mathematical concepts and techniques used in economic analysis.

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Data Engineer

Data Engineers design, build, and maintain the infrastructure that stores and processes data. They work in a variety of industries, including technology, finance, and healthcare. This course on Mathematical Methods for Data Analysis may be helpful for aspiring Data Engineers, as it provides a foundation in the mathematical concepts and techniques used in data engineering.

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Business Intelligence Analyst

Business Intelligence Analysts use their skills in data analysis to help businesses make better decisions. They collect, clean, and analyze data, and then use that data to identify trends and patterns. This course on Mathematical Methods for Data Analysis may be helpful for aspiring Business Intelligence Analysts, as it provides a foundation in the mathematical concepts and techniques used in data analysis.

See salaries and explore the career path for Business Intelligence Analyst

Reading list

We've selected 11 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Mathematical Methods for Data Analysis.

Deep Learning

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Provides a comprehensive overview of deep learning algorithms and techniques. It valuable resource for students who want to learn more about the mathematical foundations of data analysis.

Deep Learning

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Mathematical Methods for Data Analysis

What you'll learn

What's inside

Learning objectives

Syllabus

Good to know

Save this course

Activities

Career center

Reading list

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