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Joseph W. Cutrone, PhD
This course helps to build the foundational material to use mathematics as a tool to model, understand, and interpret the world around us. This is done through studying functions, their properties, and applications to data analysis. Concepts of precalculus provide the set of tools for the beginning student to begin their scientific career, preparing them for future science and calculus courses. This course is designed for all students, not just those interested in further mathematics courses. Students interested in the natural sciences, computer sciences, psychology, sociology, or similar will genuinely benefit from this introductory course, applying the skills learned to their discipline to analyze and interpret their subject material. Students will be presented with not only new ideas, but also new applications of an old subject. Real-life data, exercise sets, and regular assessments help to motivate and reinforce the content in this course, leading to learning and mastery.
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What's inside
Syllabus
Module 1: Basics and Common Functions
Functions help to study the relationship between two or more variables. They are the basic quantitative tool used to visualize, analyze, and interpret these relationships. Studying functions is the first step in developing analytics skills for mathematical modeling. In this module, we develop the concept of a function and review important algebraic operations on functions used later in this course. We will also study the important features, like domain, range, and end behavior of graphs.
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Syllabus
Module 1: Basics and Common Functions
Functions help to study the relationship between two or more variables. They are the basic quantitative tool used to visualize, analyze, and interpret these relationships. Studying functions is the first step in developing analytics skills for mathematical modeling. In this module, we develop the concept of a function and review important algebraic operations on functions used later in this course. We will also study the important features, like domain, range, and end behavior of graphs.
Read more
Traffic lights
Traffic lights
Read about what's good
what should give you pause and
possible dealbreakers
Suitable for students planning careers in natural or computer sciences, psychology, sociology, or similar fields
Appropriate for learners with no prior experience in higher mathematics
Builds a strong foundation for further scientific or calculus courses
Applies mathematical concepts to analyze data and interpret real-world problems in various disciplines
Utilizes multiple learning resources, including real-life data, exercise sets, and assessments, to promote understanding and retention
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Reviews summary
Solid precalculus foundation for stem
According to learners, this is an excellent foundational course that provides a strong base for future science and calculus studies. Many find the lectures and explanations of complex topics like functions, their properties, and inverse functions to be remarkably clear and accessible. The course effectively integrates real-world data and applications, and the exercise sets are widely praised for solidifying understanding. However, some students report that the pace can be challenging for true beginners, requiring significant self-study. Additionally, while beneficial for mastery, the assessments can be demanding.
Quizzes and homework are rigorous, testing comprehension.
"The assessments were quite challenging, which is good for learning, but sometimes felt a bit overwhelming."
"I did find the amount of time for some of the assessments a bit restrictive, but that's a minor point."
Real-world examples and practice problems enhance understanding.
"I especially appreciated the way they integrated real-world data and applications throughout."
"The emphasis on relations and functions, including their applications to data analysis, was incredibly useful."
"The exercise sets were well-designed and genuinely helped in mastery."
Prepares learners well for advanced math and STEM.
"This course was exactly what I needed to brush up on my precalculus before starting a calculus sequence."
"Overall, a very valuable course that definitely prepares you for more advanced math."
"Excellent foundational course for anyone heading into STEM."
"This course truly prepares you for higher-level math."
Lectures break down complex math concepts effectively.
"The explanations of functions, their properties, and inverse functions were incredibly clear."
"The instructor did a great job breaking down complex ideas."
"The instructor's ability to explain intricate topics in an accessible manner is commendable."
"It made complex topics like logarithms feel approachable. The structure is logical..."
Pace and depth can be difficult for new learners.
"As someone coming back to math after many years, I found myself needing to supplement the lectures..."
"I found this course quite difficult without a very strong prior math background."
"The course moves too fast for someone like me who hasn't done math in years. I ended up dropping out."
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 Precalculus: Relations and Functions with these
activities:
Algebra Review Exercises
Show steps
Practice algebra skills to strengthen your foundation.
Show steps
-
Solve equations
-
Simplify expressions
-
Graph linear functions
Review Precalculus Textbook
Show steps
Review the textbook before taking the course to refresh your memory on relevant concepts.
View
Calculus for the AP® Course
on Amazon
Show steps
-
Read through the chapter summaries
-
Complete the practice problems at the end of each chapter
-
Take notes on the main concepts
Khan Academy Precalculus Tutorials
Show steps
Follow video tutorials to reinforce your understanding of precalculus concepts.
Browse courses on
Functions
Show steps
-
Watch the videos on the basics of functions
-
Complete the practice exercises
-
Take the quizzes to test your understanding
Four other activities
Expand to see all activities and additional details
Show all seven activities
Study Group Discussions
Show steps
Engage in discussions with peers to clarify concepts and solve problems together.
Show steps
-
Form a study group with classmates
-
Meet regularly to discuss course material
-
Work together on problem sets and assignments
Function Graphing Practice
Show steps
Practice graphing functions to improve your visualization and analysis skills.
Browse courses on
Functions
Show steps
-
Plot points for a given function
-
Identify the domain and range of the function
-
Sketch the graph of the function
Exponential and Logarithmic Function Practice
Show steps
Practice working with exponential and logarithmic functions to enhance your problem-solving skills.
Browse courses on
Exponential Functions
Show steps
-
Simplify exponential expressions
-
Solve exponential equations
-
Convert between exponential and logarithmic form
Function Modeling Project
Show steps
Apply your knowledge of functions to model a real-world phenomenon.
Browse courses on
Functions
Show steps
-
Choose a phenomenon to model
-
Collect data on the phenomenon
-
Develop a mathematical function to represent the data
-
Evaluate the accuracy of the model
Algebra Review Exercises
Show steps
Practice algebra skills to strengthen your foundation.
Show steps
Show steps
Show steps
- Solve equations
- Simplify expressions
- Graph linear functions
Review Precalculus Textbook
Show steps
Review the textbook before taking the course to refresh your memory on relevant concepts.
View
Calculus for the AP® Course
on Amazon
Show steps
Show steps
Show steps
- Read through the chapter summaries
- Complete the practice problems at the end of each chapter
- Take notes on the main concepts
Khan Academy Precalculus Tutorials
Show steps
Follow video tutorials to reinforce your understanding of precalculus concepts.
Browse courses on
Functions
Show steps
Show steps
Show steps
- Watch the videos on the basics of functions
- Complete the practice exercises
- Take the quizzes to test your understanding
Four other activities
Expand to see all activities and additional details
Show all seven activities
Study Group Discussions
Show steps
Engage in discussions with peers to clarify concepts and solve problems together.
Show steps
Show steps
Show steps
- Form a study group with classmates
- Meet regularly to discuss course material
- Work together on problem sets and assignments
Function Graphing Practice
Show steps
Practice graphing functions to improve your visualization and analysis skills.
Browse courses on
Functions
Show steps
Show steps
Show steps
- Plot points for a given function
- Identify the domain and range of the function
- Sketch the graph of the function
Exponential and Logarithmic Function Practice
Show steps
Practice working with exponential and logarithmic functions to enhance your problem-solving skills.
Browse courses on
Exponential Functions
Show steps
Show steps
Show steps
- Simplify exponential expressions
- Solve exponential equations
- Convert between exponential and logarithmic form
Function Modeling Project
Show steps
Apply your knowledge of functions to model a real-world phenomenon.
Browse courses on
Functions
Show steps
Show steps
Show steps
- Choose a phenomenon to model
- Collect data on the phenomenon
- Develop a mathematical function to represent the data
- Evaluate the accuracy of the model
Career center
Learners who complete Precalculus: Relations and Functions will develop knowledge and skills
that may be useful to these careers:
Data Scientist
Data Scientist
Data Scientists use scientific methods, algorithms, and systems to extract knowledge and insights from data in various forms, both structured and unstructured. Taking the Precalculus: Relations and Functions course can help you build a strong foundation for success in this field. The course provides a comprehensive understanding of functions, their properties, and applications to data analysis. This knowledge is essential for Data Scientists who need to analyze and interpret large datasets effectively.
Statistician
Statistician
Statisticians collect, analyze, interpret, and present data to help businesses and organizations make informed decisions. As a Statistician, you would need a strong foundation in mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in data analysis. This knowledge will be beneficial for your career as a Statistician.
Financial Analyst
Financial Analyst
Financial Analysts use mathematical and statistical techniques to analyze financial data and make recommendations on investments. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in financial analysis. This knowledge will be beneficial for your career as a Financial Analyst.
Actuary
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty in various fields, including insurance, finance, and healthcare. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in actuarial science. This knowledge will be beneficial for your career as an Actuary.
Economist
Economist
Economists use mathematical and statistical techniques to analyze economic data and make recommendations on economic policy. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in economics. This knowledge will be beneficial for your career as an Economist.
Market Researcher
Market Researcher
Market Researchers collect, analyze, and interpret data to understand consumer behavior and market trends. They need a strong understanding of mathematics, including statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in market research. This knowledge will be beneficial for your career as a Market Researcher.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and statistical techniques to analyze complex systems and make recommendations for improvement. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in operations research. This knowledge will be beneficial for your career as an Operations Research Analyst.
Business Analyst
Business Analyst
Business Analysts use data analysis and problem-solving skills to improve business processes and make recommendations for change. They need a strong understanding of mathematics, including statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in business analysis. This knowledge will be beneficial for your career as a Business Analyst.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software applications. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in software engineering. This knowledge will be beneficial for your career as a Software Engineer.
Data Analyst
Data Analyst
Data Analysts collect, clean, and analyze data to find trends and patterns. They need a strong understanding of mathematics, including statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in data analysis. This knowledge will be beneficial for your career as a Data Analyst.
Computer Scientist
Computer Scientist
Computer Scientists design, develop, and implement computer systems. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in computer science. This knowledge will be beneficial for your career as a Computer Scientist.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze financial data and make recommendations on investments. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in quantitative analysis. This knowledge will be beneficial for your career as a Quantitative Analyst.
Risk Analyst
Risk Analyst
Risk Analysts use mathematical and statistical techniques to assess risk and uncertainty in various fields, including insurance, finance, and healthcare. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in risk analysis. This knowledge will be beneficial for your career as a Risk Analyst.
Mathematician
Mathematician
Mathematicians develop new mathematical theories and solve mathematical problems. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in mathematics. This knowledge will be beneficial for your career as a Mathematician.
Teacher
Teacher
Teachers educate students in various subjects, including mathematics. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in teaching. This knowledge will be beneficial for your career as a Teacher.
For more career information including salaries, visit:
OpenCourser.com/course/6a2d2e/precalculus
Reading list
We've selected seven 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
Precalculus: Relations and Functions.
Provides a comprehensive introduction to the concepts and applications of precalculus, including functions, graphs, and trigonometry. It valuable resource for students who need a strong foundation in precalculus before taking calculus.
Provides a comprehensive introduction to the concepts and applications of precalculus, including functions, graphs, and trigonometry. It valuable resource for students who need a strong foundation in precalculus before taking calculus.
Provides a comprehensive introduction to the concepts and applications of calculus, including limits, derivatives, and integrals. It valuable resource for students who need a strong foundation in calculus after taking precalculus.
Provides a comprehensive review of college algebra and trigonometry, including functions, equations, inequalities, and trigonometry. It valuable resource for students who need a refresher on these topics before taking precalculus.
Provides a comprehensive introduction to the concepts and applications of college algebra. It valuable resource for students who need a strong foundation in college algebra before taking precalculus.
Save
Provides a comprehensive introduction to the concepts and applications of trigonometry. It valuable resource for students who need a strong foundation in trigonometry before taking precalculus.
Provides a comprehensive introduction to trigonometry, including the unit circle, trigonometric functions, and their applications. It valuable resource for students who need a strong foundation in trigonometry before taking precalculus.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/6a2d2e/precalculus
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Level
Introductory
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Coursera
Institution
Johns Hopkins University
Instructor
Joseph W. Cutrone, PhD
Language
English
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This course belongs to a
collection
called
Precalculus through Data and Modelling. It's comprised of three courses:
- Precalculus: Mathematical Modeling
- Precalculus: Periodic Functions
- Precalculus: Relations and Functions (viewing)
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