Complete Mathematics Masterclass: College & University Level from Udemy

This course is for everyone who wants to learn applied mathematics on a college and university level. It is a complete course containing all relevant topics like Calculus, Algebra, Statistics & Stochastics.

Advanced mathematics is relevant in many fields: Programming & IT, Engineering, Science (Physics, Chemistry, Biology, Pharmacy, ...), Business & Economics. This course will teach you all you have to know in 24 hours.

You are kindly invited to join this carefully prepared course in which we derive the following concepts from scratch. I will present examples and give you exercises (incl. solutions) for all topics.

College-level mathematics (10 hours)

Limits of functions
Derivatives & Integrals in 1 dimension
Vectors in cartesian coordinates
Stochastic & Probability distributions

University-level mathematics (14 hours)

Sequences & Series
Taylor expansions
Complex numbers
Derivatives & Integrals in multiple dimensions
Alternative coordinate systems
Differential equations
Matrix algebra
Fourier transforms & Delta distribution

Why me?

My name is Börge Göbel and I am a postdoc working as a scientist in theoretical physics. I have refined my advisor skills as a tutor of Bachelor, Master and PhD students in theoretical physics and have other successful courses here on Udemy.

I always had a passion for the mathematical side of science. Still today, I use the concepts of this course on a daily basis when I am programing on the PC or when I have to solve mathematical problems analytically on a sheet of paper.

I hope you are excited and I kindly welcome you to our course.

What's inside

Syllabus

[Pilot Section] If you just finished school: What you know & what you will learn

Overview of the course

Overview image

Section intro

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Covers calculus, algebra, and statistics, which are foundational for science, technology, engineering, and mathematics, providing a strong base for further study

Bridges the gap between high school and higher education by reviewing fundamental concepts and introducing more advanced topics, which can ease the transition

Taught by a postdoc in theoretical physics, who uses these mathematical concepts daily in programming and problem-solving, which can provide valuable insights

Includes a pilot section reviewing basic functions and vector algebra, which helps learners identify gaps in their knowledge and build a solid foundation

Includes add-on lectures on calculating derivatives and integrals numerically with Python, which can be useful for applying mathematical concepts in real-world scenarios

Requires learners to understand limits, derivatives, and integrals in one dimension before moving on to university-level mathematics, which may require additional preparation

Reviews summary

Comprehensive college & university math overview

According to learners, this course provides a comprehensive overview of college and university-level mathematics topics, including Calculus, Algebra, Statistics, and Differential Equations. Many find the instructor's explanations clear and effective, appreciating his passion for the subject. The course is often described as a good starting point or review for various fields requiring advanced math. However, some learners note that certain topics might be covered too briefly or lack sufficient depth, suggesting it may serve better as an introduction or refresher rather than a complete mastery course for all subjects covered. The exercises and solutions are generally seen as helpful for reinforcing understanding.

Pace suits some, challenging for others.

"The pace was just right for me, covering a lot without getting bogged down."

"Some found the pace a bit fast, especially if they had limited prior exposure."

"It moves quickly through certain complex ideas, requiring focus."

"The difficulty is appropriate for an introductory college level, but maybe less so for advanced university study."

"Requires some prior high school math background to keep up."

Exercises helpful but sometimes limited.

"The exercises provided are helpful for practicing the concepts taught."

"I liked having exercises with solutions to test my understanding."

"The exercises helped solidify the lectures, though more practice problems would be beneficial."

"Solutions were provided which was great, but I felt there weren't enough exercises for every topic."

"Good for basic practice, but might not be sufficient for challenging university problems."

Excellent for beginners or refreshing knowledge.

"This is an excellent course for someone who is just starting out in college math or needs a good review."

"It's perfect if you need to refresh your memory on various math topics before university."

"A solid foundation is provided, making it suitable for beginners."

"Great as a primer or to brush up on forgotten concepts."

"I used it to prepare for my university classes and found it very helpful."

Explanations are clear and easy to follow.

"The instructor explains complex topics in a way that is easy to understand."

"Börge is a great teacher, clear and enthusiastic."

"I found the explanations to be very clear and concise, which is crucial for dense math topics."

"His teaching style makes difficult concepts accessible."

"The lectures are well-structured and the explanations are simple yet effective."

Wide range of advanced math topics covered.

"It covers a wide array of advanced math topics relevant for college and university, acting as a great overview."

"The course definitely lives up to its title covering calculus, linear algebra, differential equations and more."

"I found the course to be very comprehensive, touching upon most major areas of higher mathematics I needed a refresher on."

"I appreciate the sheer breadth of the subjects included; it's like a condensed math curriculum."

"The syllabus is impressive in its scope for a single course."

Some topics covered too briefly for mastery.

"While comprehensive in breadth, some topics lack the depth needed for true mastery."

"Certain sections feel rushed, and I needed external resources for deeper understanding."

"It's a good overview, but don't expect extremely detailed explanations on every single concept."

"I wish some areas like differential equations had more in-depth coverage."

"Could use more examples for complex topics."

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 Complete Mathematics Masterclass: College & University Level with these activities:

Review Algebra Fundamentals

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Strengthen your understanding of core algebraic concepts. A solid foundation in algebra is crucial for success in calculus and other advanced math topics covered in this course.

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Review key concepts and formulas.
Work through practice problems.
Identify areas of weakness and seek additional resources.

Review Calculus Textbook

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Reinforce your understanding of calculus concepts. This book will help you to master the calculus concepts presented in the course.

View Biocalculus: Calculus, Probability, and... on Amazon

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Read the relevant chapters on limits, derivatives, and integrals.
Work through the examples and exercises in the book.
Compare the book's explanations with the course lectures.

Practice Differentiation and Integration

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Sharpen your calculus skills through repetitive exercises. Consistent practice with differentiation and integration will improve your speed and accuracy in solving problems.

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Find online resources with calculus practice problems.
Work through a set number of problems each day.
Check your answers and review any mistakes.

Four other activities

Expand to see all activities and additional details

Show all seven activities

Create a Cheat Sheet for Integration Techniques

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Summarize key integration techniques in a concise format. Creating a cheat sheet will help you to consolidate your knowledge and quickly recall important formulas and methods.

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Review the different integration techniques covered in the course.
Organize the techniques into categories.
Write down the formulas and steps for each technique.
Design a visually appealing and easy-to-use cheat sheet.

Model a Real-World Phenomenon with Differential Equations

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Apply your knowledge of differential equations to a practical problem. This project will allow you to see how mathematical concepts can be used to model and understand real-world phenomena.

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Choose a phenomenon that can be modeled with differential equations.
Develop a mathematical model of the phenomenon.
Solve the differential equation and analyze the results.
Present your findings in a report or presentation.

Explore Linear Algebra

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Deepen your understanding of linear algebra concepts. This book will help you to master the matrix algebra concepts presented in the course.

View Linear Algebra and Its Applications on Amazon

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Read the relevant chapters on matrices, vectors, and linear transformations.
Work through the examples and exercises in the book.
Relate the book's explanations to the course lectures.

Develop a Fourier Transform Visualizer

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Create a tool to visualize Fourier transforms. This project will solidify your understanding of Fourier transforms and their applications.

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Learn about Fourier transforms and their properties.
Choose a programming language and libraries for visualization.
Implement the Fourier transform algorithm.
Create a user interface to input signals and display their Fourier transforms.

Career center

Learners who complete Complete Mathematics Masterclass: College & University Level will develop knowledge and skills that may be useful to these careers:

Research Scientist

A research scientist conducts scientific research, often in a specific field such as physics, chemistry, or biology. They design experiments, collect data, and analyze results. This career typically requires an advanced degree. Many scientific disciplines rely heavily on advanced mathematics for modeling and analysis. This course covers a wide range of mathematical topics relevant to research scientists, like differential equations, Fourier transforms, and statistical analysis. The course may be particularly useful to those working in quantitative fields of research.

See salaries and explore the career path for Research Scientist

Bioinformatician

A bioinformatician develops and applies computational tools and methods to analyze biological data. This requires a strong foundation in mathematics, statistics, and computer science. This course may be useful because it covers essential mathematical concepts like linear algebra, calculus, and stochastic processes, which are relevant to analyzing genomic data, building predictive models, and understanding complex biological systems. The sections on statistics and stochastic processes, as well as matrix algebra, help the bioinformatician.

See salaries and explore the career path for Bioinformatician

Quantitative Analyst

A quantitative analyst, often working in the finance industry, develops and implements mathematical models for pricing, trading, and risk management. This career frequently requires a master's degree, or even a PhD. The mathematical concepts covered in this course, such as calculus, differential equations, and matrix algebra, are directly applicable to the models used by quantitative analysts. Understanding Taylor expansions and Fourier transforms, as taught in this course, helps the quantitative analyst analyze financial data and develop sophisticated trading strategies. Aspiring quantitative analysts may find this course useful as a refresher.

See salaries and explore the career path for Quantitative Analyst

Statistician

A statistician collects, analyzes, and interprets data to identify trends and patterns. Statisticians apply mathematical and statistical techniques to solve problems in a variety of fields, including healthcare, business, and government. This course offers a great introduction to many of the mathematical concepts that will be used by statisticians on a daily basis. A future statistician may appreciate learning about probability distributions and matrix algebra, as well as stochastic.

See salaries and explore the career path for Statistician

Machine Learning Engineer

A machine learning engineer designs, develops, and deploys machine learning models. This role requires a strong foundation in mathematics, particularly linear algebra, calculus, and statistics. This course covers these topics, providing aspiring machine learning engineers with the mathematical tools and knowledge needed to understand and implement machine learning algorithms. The course may be especially useful for learning about derivatives, integrals, and probability distributions.

See salaries and explore the career path for Machine Learning Engineer

Actuary

An actuary assesses and manages financial risks, typically for insurance companies and pension funds. Actuaries rely heavily on mathematical and statistical models to predict future events and determine appropriate pricing and reserves. A strong understanding of probability distributions, calculus, and financial mathematics is essential for this role. This course provides a foundational knowledge of these areas, including stochastic and probability distributions. Aspiring actuaries may find this course a helpful refresher.

See salaries and explore the career path for Actuary

Operations Research Analyst

An operations research analyst uses mathematical and analytical methods to help organizations make better decisions. They develop models and algorithms to optimize processes, improve efficiency, and solve complex problems. This role requires a strong understanding of linear algebra, calculus, and optimization techniques. This course may be useful because it provides a comprehensive overview of these topics, including matrix algebra, differential equations, and derivatives and integrals in multiple dimensions.

See salaries and explore the career path for Operations Research Analyst

Data Scientist

A data scientist analyzes complex datasets to extract meaningful insights and develop predictive models. This often requires a strong foundation in mathematics, particularly statistics and calculus. This course touches on calculus, algebra, and stochastics. With a solid grasp of these concepts, a data scientist is better equipped to understand the underlying principles of machine learning algorithms and interpret data effectively. The course gives potential data scientists exposure to limits, derivatives, and integrals, all of which help build a good footing in the field.

See salaries and explore the career path for Data Scientist

Economist

An economist studies the production, distribution, and consumption of goods and services. Economists develop and use mathematical models to analyze economic trends, forecast future conditions, and advise policymakers. A solid foundation in calculus, statistics, and econometrics is essential for this role. This course may be useful by providing the learner with those tools, helping the economist better comprehend economic models and analyze data effectively. Aspiring economists may find the sections on derivatives, integrals, and probability distributions particularly relevant.

See salaries and explore the career path for Economist

Financial Analyst

A financial analyst analyzes financial data, provides investment recommendations, and helps businesses make informed decisions. Financial analysts use mathematical models and statistical techniques to evaluate investment opportunities and manage risk. This course provides a good foundation in calculus, algebra, and stochastics. Learning about sequences and series, as well as derivatives and integrals, can enhance a financial analyst's ability to interpret financial data and construct financial models.

See salaries and explore the career path for Financial Analyst

Game Developer

A game developer creates video games for various platforms. Game developers need a solid understanding of mathematics, particularly linear algebra and calculus, to create realistic graphics, physics simulations, and artificial intelligence. This course provides a strong foundation in these areas, including vector algebra, coordinate systems, and derivatives and integrals. The sections on linear algebra and calculus may be very practical for aspiring game developers.

See salaries and explore the career path for Game Developer

Software Engineer

Software engineers design, develop, and test software applications. While not always immediately apparent, mathematics plays a crucial role in many areas of software engineering, especially in fields like game development, computer graphics, and data science. This course covers essential mathematical concepts like linear algebra, calculus, and statistics, all of which help when developing efficient algorithms and solving complex problems. The topics on vector algebra and coordinate systems included in this course help software engineers working on graphics applications.

See salaries and explore the career path for Software Engineer

Civil Engineer

Civil engineers design, construct, and maintain infrastructure projects such as roads, bridges, and buildings. A solid understanding of mathematics, including calculus, linear algebra, and differential equations, is essential for analyzing structural loads, designing stable structures, and managing projects effectively. This course may be useful by reinforcing these core mathematical concepts. Aspiring civil engineers may find the sections on vector algebra and differential equations particularly relevant.

See salaries and explore the career path for Civil Engineer

Mechanical Engineer

Mechanical engineers design, develop, and test mechanical devices and systems. Mechanical engineering relies heavily on mathematical principles, particularly calculus, differential equations, and linear algebra. This course provides a strong foundation in these areas, which may be key for mechanical engineers in modeling and analyzing complex systems. The course may be especially useful for mechanical engineers to brush up on differential equations and calculus.

See salaries and explore the career path for Mechanical Engineer

Financial Planner

A financial planner helps individuals and families manage their finances and achieve their financial goals. They provide advice on investments, retirement planning, insurance, and other financial matters. While this role is more client-facing, a solid grasp of mathematics is helpful for understanding financial products and developing effective financial plans. This course may be useful by giving the financial planner a good foundation in algebra and statistics.

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Physics Teacher

A physics teacher educates students in the principles of physics. They present information by lecture, demonstration, discussion, and assignments. This course may be helpful to teachers by providing them with a comprehensive understanding of the college and university level mathematics that underlies physics. This course helps physics teachers teach mathematical methods and reasoning necessary for solving physics problems. The thorough nature of this course may prove valuable in keeping educators prepared.

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Reading list

We've selected two 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 Complete Mathematics Masterclass: College & University Level.

Biocalculus: Calculus, Probability, and Statistics...

Save

Provides a comprehensive introduction to calculus. It covers limits, derivatives, integrals, sequences, and series in detail. It valuable reference for understanding the calculus concepts presented in the course, and it is commonly used as a textbook in many universities.

Biocalculus: Calculus, Probability, and Statistics...

Loose Leaf

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Linear Algebra and Its Applications

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Provides a thorough introduction to linear algebra. It covers matrices, vectors, linear transformations, eigenvalues, and eigenvectors. It useful reference for understanding the matrix algebra concepts presented in the course, and it is commonly used as a textbook in many universities.

Linear Algebra and Its Applications

Paperback

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Linear Algebra and Its Applications

Kindle Edition

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