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Martin Anthony
Mathematics 1 Part 2 is the second of two self-paced courses from LSE which aim to introduce and develop and understanding of essential mathematical concepts, methods and techniques. This course can be taken alone or as part of the LSE MicroBachelors program in Mathematics and Statistics Fundamentals.
Part 2 covers the following topics:
-
Integration
-
Profit maximisation
-
Constrained optimisation
-
Matrices, vectors, and linear equations
-
Sequences, series, and financial modelling
Read more
Mathematics 1 Part 2 is the second of two self-paced courses from LSE which aim to introduce and develop and understanding of essential mathematical concepts, methods and techniques. This course can be taken alone or as part of the LSE MicroBachelors program in Mathematics and Statistics Fundamentals.
Part 2 covers the following topics:
-
Integration
-
Profit maximisation
-
Constrained optimisation
-
Matrices, vectors, and linear equations
-
Sequences, series, and financial modelling
Read more
Mathematics 1 Part 2 is the second of two self-paced courses from LSE which aim to introduce and develop and understanding of essential mathematical concepts, methods and techniques. This course can be taken alone or as part of the LSE MicroBachelors program in Mathematics and Statistics Fundamentals.
Part 2 covers the following topics:
-
Integration
-
Profit maximisation
-
Constrained optimisation
-
Matrices, vectors, and linear equations
-
Sequences, series, and financial modelling
This course will equip you with the skills to solve unseen mathematical problems in these areas and will emphasise their applications to problems in economics, management, and related areas.
What you'll learn
By the end of this course you will have:
- used the concepts, terminology, methods and conventions covered in the course to solve mathematical problems
- the ability to solve unseen mathematical problems involving understanding of these concepts and application of these methods
- seen how mathematical techniques can be used to solve problems in economics and related subjects
- acquired skills in the methods of calculus (including multivariate calculus) and linear algebra, as required for their use in economics-based subjects
Register for this course and see more details by visiting:
OpenCourser.com/course/qzzww4/mathematics
What's inside
Learning objectives
- Used the concepts, terminology, methods and conventions covered in the course to solve mathematical problems
- The ability to solve unseen mathematical problems involving understanding of these concepts and application of these methods
- Seen how mathematical techniques can be used to solve problems in economics and related subjects
- Acquired skills in the methods of calculus (including multivariate calculus) and linear algebra, as required for their use in economics-based subjects
- Used the concepts, terminology, methods and conventions covered in the course to solve mathematical problems
- The ability to solve unseen mathematical problems involving understanding of these concepts and application of these methods
- Seen how mathematical techniques can be used to solve problems in economics and related subjects
- Acquired skills in the methods of calculus (including multivariate calculus) and linear algebra, as required for their use in economics-based subjects
Syllabus
Integration
Profit maximisation
Constrained optimisation
Matrices, vectors, and linear equations
Read more
Syllabus
Integration
Profit maximisation
Constrained optimisation
Matrices, vectors, and linear equations
Read more
Traffic lights
Traffic lights
Read about what's good
what should give you pause and
possible dealbreakers
Demands familiarity with basic mathematics, such as Algebra and Calculus
Assumes that learners already understand basic statistics
Taught by instructors who have experience in teaching Maths at the university level
Provides learners with the opportunity to practice maths on real-world problems
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Save this course to your list so you can find it easily later.
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Reviews summary
Integral calculus and linear algebra for economics
According to students, this course offers a rigorous and demanding exploration of mathematics, particularly for those in economics and related fields. Learners consistently highlight the highly relevant applications to economics and financial modeling, finding them practical and insightful. While many praise the clear lectures and accessible explanations, some note that the pace can be too fast and certain topics may require external resources for deeper understanding, suggesting it's best suited for serious learners with a strong foundation. The problem sets are often described as challenging yet incredibly helpful for reinforcing concepts.
Some sections less engaging, occasionally lacking sufficient depth.
"...some of the explanations for complex topics could be more detailed, requiring external resources for deeper understanding."
"It felt a bit dry and less engaging than I hoped. The examples provided were sometimes too simple..."
"I wished for more interactive elements or detailed solutions to problems."
Assignments are challenging but effective for concept reinforcement.
"I found the problem sets challenging but incredibly helpful for cementing the concepts."
"The assignments reinforced learning well."
"The exercises are well-designed to build understanding."
Instructor's explanations make complex topics accessible.
"The lectures are clear and the examples are very practical, especially the financial modeling sections."
"The instructor's explanations are top-notch, making difficult concepts accessible."
"The explanations for integral calculus are very clear..."
Emphasizes real-world use in economics and finance.
"The applications to economics are well-explained and highly relevant."
"The real-world applications truly make the concepts stick."
"Highly recommend! The course dives deep into crucial mathematical concepts with a focus on real-world applications in economics."
"I learned how mathematical techniques can be used to solve problems in economics and related subjects."
Some find the course too fast and difficult without strong prerequisites.
"I found this course extremely difficult to follow. The pace was too fast for me..."
"...assumes a very strong mathematical background from Part 1, and if you're rusty, you'll find it challenging."
"Not for beginners, despite being 'Part 2' of an introductory series."
"Some parts felt rushed, requiring external resources for deeper understanding."
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 Mathematics 1 Part 2: Integral calculus, algebra, and applications with these
activities:
Volunteer as a Math Tutor at a Local School or Organization
Show steps
Tutoring students will not only reinforce your understanding of the concepts but also enhance your communication and problem-solving skills.
Browse courses on
Mathematics
Show steps
-
Identify a local school or organization in need of volunteer tutors
-
Apply for the volunteer position
-
Meet with students regularly to provide support and guidance
-
Evaluate students' progress and provide feedback
Review Single & Multivariable Calculus
Show steps
Calculus, especially in its multivariate form, is a key skill for Economics. Prior experience will make it easier to succeed in the course.
Browse courses on
Calculus
Show steps
-
Review the chain rule for single-variable functions.
-
Review integration techniques for single-variable functions, including u-substitution and integration by parts.
-
Review partial derivatives and directional derivatives.
-
Review multiple integrals, including double and triple integrals.
Read 'Mathematics for Economics and Finance' by Michael Hoy
Show steps
This book provides a comprehensive overview of the mathematical concepts covered in the course, offering additional examples and practice problems to enhance your understanding.
View
Student Solutions Manual for Mathematics for...
on Amazon
Show steps
-
Identify the chapters relevant to the course topics
-
Read the assigned chapters thoroughly
-
Work through the practice problems provided
-
Take notes and highlight important concepts
12 other activities
Expand to see all activities and additional details
Show all 15 activities
Join a Study Group for Matrix Algebra and Linear Equations
Show steps
Collaborating with peers in a study group will allow you to share knowledge, discuss different perspectives, and enhance your problem-solving skills.
Browse courses on
Matrices
Show steps
-
Find a group of classmates with diverse strengths
-
Meet regularly to discuss the course material
-
Work together to solve practice problems
-
Provide feedback and support to each other
Form a study group with other students in the course.
Show steps
Study groups can provide a supportive and collaborative learning environment.
Show steps
-
Find a few other students in the course who are interested in forming a study group.
-
Decide how often you will meet and where you will meet.
-
Set up a schedule for your study sessions.
-
Come to each study session prepared to discuss the course material.
Participate in online discussion forums related to the course material.
Show steps
Online discussion forums can provide a platform for students to ask questions, share ideas, and collaborate with their peers.
Show steps
-
Find an online discussion forum related to the course material.
-
Create an account and join the forum.
-
Post questions or comments to the forum.
-
Respond to other students' posts.
Explore Different Integration Techniques Online
Show steps
By following online tutorials, you can deepen your understanding of various integration techniques and enhance your problem-solving ability.
Browse courses on
Integration
Show steps
-
Identify areas where you need additional practice
-
Find reputable online tutorials
-
Work through the tutorials step-by-step
-
Apply the techniques to solve practice problems
Follow online tutorials on constrained optimization.
Show steps
Useful for understanding one of the more challenging concepts covered in the course.
Browse courses on
Constrained Optimization
Show steps
-
Find a reputable online tutorial on constrained optimization using Lagrange multipliers.
-
Follow the tutorial step-by-step, taking notes and working through the examples.
-
Complete any practice problems or exercises provided in the tutorial.
Solve practice problems on integration and profit maximization.
Show steps
Solving practice problems can help you to master the key concepts and techniques covered in the course.
Browse courses on
Integration
Show steps
-
Find a textbook or online resource that provides practice problems on integration.
-
Select several problems that cover different types of integrals.
-
Solve the problems, showing all of your work.
-
Check your answers against the solutions provided in the textbook or online resource.
Solve practice problems on constrained optimization using Lagrange multipliers.
Show steps
Solving practice problems, especially on more challenging topics, can help improve your problem-solving skills:
Browse courses on
Constrained Optimization
Show steps
-
Find a textbook or online resource that provides practice problems on constrained optimization using Lagrange multipliers.
-
Select several problems that cover different types of constraints.
-
Solve the problems, showing all of your work.
-
Check your answers against the solutions provided in the textbook or online resource.
Solve Optimization Problems Using Calculus
Show steps
Regular practice in solving optimization problems will sharpen your analytical skills and improve your ability to find optimal solutions in economics and management.
Browse courses on
Constrained Optimization
Show steps
-
Review the concepts of constrained optimization
-
Identify the objective function and constraints
-
Apply calculus techniques to solve for the optimal solution
-
Interpret the results in the context of the problem
Create a Concept Map of Sequences and Series
Show steps
Developing a concept map will help you visualize the relationships between different concepts and improve your overall understanding of sequences and series.
Browse courses on
Sequences
Show steps
-
Identify the key concepts related to sequences and series
-
Create a visual representation of the concepts
-
Connect the concepts with arrows or lines
-
Label the connections with brief explanations
Build a Financial Model Using Integration and Matrices
Show steps
Creating a financial model will help you apply the concepts of integration and matrices to a practical business problem, solidifying your understanding.
Browse courses on
Integration
Show steps
-
Define the problem and gather data
-
Choose the appropriate integration technique
-
Construct the financial model using matrices
-
Analyze the results and make recommendations
Create a blog post summarizing the key concepts of the course.
Show steps
Creating content can solidify your understanding
Show steps
-
Choose a topic from the course material that you are particularly interested in.
-
Write a blog post that summarizes the key concepts of the topic.
-
Publish your blog post online.
Contribute to Open-Source Projects Related to Mathematics
Show steps
Involving yourself in open-source projects will not only enhance your programming skills but also allow you to apply mathematical concepts in a practical context.
Browse courses on
Mathematics
Show steps
-
Identify open-source projects related to mathematics
-
Review the project code and documentation
-
Identify areas where you can contribute
-
Submit your contributions for review
Volunteer as a Math Tutor at a Local School or Organization
Show steps
Tutoring students will not only reinforce your understanding of the concepts but also enhance your communication and problem-solving skills.
Browse courses on
Mathematics
Show steps
Show steps
Show steps
- Identify a local school or organization in need of volunteer tutors
- Apply for the volunteer position
- Meet with students regularly to provide support and guidance
- Evaluate students' progress and provide feedback
Review Single & Multivariable Calculus
Show steps
Calculus, especially in its multivariate form, is a key skill for Economics. Prior experience will make it easier to succeed in the course.
Browse courses on
Calculus
Show steps
Show steps
Show steps
- Review the chain rule for single-variable functions.
- Review integration techniques for single-variable functions, including u-substitution and integration by parts.
- Review partial derivatives and directional derivatives.
- Review multiple integrals, including double and triple integrals.
Read 'Mathematics for Economics and Finance' by Michael Hoy
Show steps
This book provides a comprehensive overview of the mathematical concepts covered in the course, offering additional examples and practice problems to enhance your understanding.
View
Student Solutions Manual for Mathematics for...
on Amazon
Show steps
Show steps
Show steps
- Identify the chapters relevant to the course topics
- Read the assigned chapters thoroughly
- Work through the practice problems provided
- Take notes and highlight important concepts
12 other activities
Expand to see all activities and additional details
Show all 15 activities
Join a Study Group for Matrix Algebra and Linear Equations
Show steps
Collaborating with peers in a study group will allow you to share knowledge, discuss different perspectives, and enhance your problem-solving skills.
Browse courses on
Matrices
Show steps
Show steps
Show steps
- Find a group of classmates with diverse strengths
- Meet regularly to discuss the course material
- Work together to solve practice problems
- Provide feedback and support to each other
Form a study group with other students in the course.
Show steps
Study groups can provide a supportive and collaborative learning environment.
Show steps
Show steps
Show steps
- Find a few other students in the course who are interested in forming a study group.
- Decide how often you will meet and where you will meet.
- Set up a schedule for your study sessions.
- Come to each study session prepared to discuss the course material.
Participate in online discussion forums related to the course material.
Show steps
Online discussion forums can provide a platform for students to ask questions, share ideas, and collaborate with their peers.
Show steps
Show steps
Show steps
- Find an online discussion forum related to the course material.
- Create an account and join the forum.
- Post questions or comments to the forum.
- Respond to other students' posts.
Explore Different Integration Techniques Online
Show steps
By following online tutorials, you can deepen your understanding of various integration techniques and enhance your problem-solving ability.
Browse courses on
Integration
Show steps
Show steps
Show steps
- Identify areas where you need additional practice
- Find reputable online tutorials
- Work through the tutorials step-by-step
- Apply the techniques to solve practice problems
Follow online tutorials on constrained optimization.
Show steps
Useful for understanding one of the more challenging concepts covered in the course.
Browse courses on
Constrained Optimization
Show steps
Show steps
Show steps
- Find a reputable online tutorial on constrained optimization using Lagrange multipliers.
- Follow the tutorial step-by-step, taking notes and working through the examples.
- Complete any practice problems or exercises provided in the tutorial.
Solve practice problems on integration and profit maximization.
Show steps
Solving practice problems can help you to master the key concepts and techniques covered in the course.
Browse courses on
Integration
Show steps
Show steps
Show steps
- Find a textbook or online resource that provides practice problems on integration.
- Select several problems that cover different types of integrals.
- Solve the problems, showing all of your work.
- Check your answers against the solutions provided in the textbook or online resource.
Solve practice problems on constrained optimization using Lagrange multipliers.
Show steps
Solving practice problems, especially on more challenging topics, can help improve your problem-solving skills:
Browse courses on
Constrained Optimization
Show steps
Show steps
Show steps
- Find a textbook or online resource that provides practice problems on constrained optimization using Lagrange multipliers.
- Select several problems that cover different types of constraints.
- Solve the problems, showing all of your work.
- Check your answers against the solutions provided in the textbook or online resource.
Solve Optimization Problems Using Calculus
Show steps
Regular practice in solving optimization problems will sharpen your analytical skills and improve your ability to find optimal solutions in economics and management.
Browse courses on
Constrained Optimization
Show steps
Show steps
Show steps
- Review the concepts of constrained optimization
- Identify the objective function and constraints
- Apply calculus techniques to solve for the optimal solution
- Interpret the results in the context of the problem
Create a Concept Map of Sequences and Series
Show steps
Developing a concept map will help you visualize the relationships between different concepts and improve your overall understanding of sequences and series.
Browse courses on
Sequences
Show steps
Show steps
Show steps
- Identify the key concepts related to sequences and series
- Create a visual representation of the concepts
- Connect the concepts with arrows or lines
- Label the connections with brief explanations
Build a Financial Model Using Integration and Matrices
Show steps
Creating a financial model will help you apply the concepts of integration and matrices to a practical business problem, solidifying your understanding.
Browse courses on
Integration
Show steps
Show steps
Show steps
- Define the problem and gather data
- Choose the appropriate integration technique
- Construct the financial model using matrices
- Analyze the results and make recommendations
Create a blog post summarizing the key concepts of the course.
Show steps
Creating content can solidify your understanding
Show steps
Show steps
Show steps
- Choose a topic from the course material that you are particularly interested in.
- Write a blog post that summarizes the key concepts of the topic.
- Publish your blog post online.
Contribute to Open-Source Projects Related to Mathematics
Show steps
Involving yourself in open-source projects will not only enhance your programming skills but also allow you to apply mathematical concepts in a practical context.
Browse courses on
Mathematics
Show steps
Show steps
Show steps
- Identify open-source projects related to mathematics
- Review the project code and documentation
- Identify areas where you can contribute
- Submit your contributions for review
Career center
Learners who complete Mathematics 1 Part 2: Integral calculus, algebra, and applications will develop knowledge and skills
that may be useful to these careers:
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze financial data and make investment decisions. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the core mathematical and analytical skills needed to succeed in this role. It will equip you with the tools to analyze data, build models, and make informed investment decisions.
Actuary
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty in the insurance and finance industries. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the core mathematical and analytical skills needed to succeed in this field, including probability, statistics, and financial modeling.
Risk Manager
Risk Manager
Risk Managers use mathematical and analytical skills to assess and manage risk in businesses and organizations. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the foundation in probability, statistics, and financial modeling that is necessary for this field. It will equip you with the tools to analyze data, build models, and make informed recommendations to businesses and organizations.
Data Scientist
Data Scientist
Data Scientists use mathematical and analytical skills to extract insights from large datasets. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the foundation in calculus, linear algebra, and statistical modeling that is essential for this role. It will equip you with the skills to analyze data, build models, and communicate insights to stakeholders.
Economist
Economist
Economists use mathematical and analytical skills to study the economy and make recommendations on economic policy. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the foundation in calculus, optimization, and linear algebra that is necessary for this field. It will equip you with the tools to analyze economic data, build models, and make informed predictions.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical skills to improve the efficiency of business operations. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the foundation in optimization, linear algebra, and probability that is necessary for this field. It will equip you with the tools to analyze data, build models, and make informed recommendations to businesses.
Market Researcher
Market Researcher
Market Researchers use mathematical and analytical skills to understand consumer behavior and market trends. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the foundation in calculus, statistics, and linear algebra that is necessary for this field. It will equip you with the tools to analyze data, build models, and make informed recommendations to businesses.
Business Analyst
Business Analyst
Business Analysts use mathematical and analytical skills to identify and solve business problems. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the foundation in calculus, statistics, and linear algebra that is necessary for this field. It will equip you with the tools to analyze data, build models, and make informed recommendations to businesses.
Statistician
Statistician
Statisticians use mathematical and analytical skills to collect, analyze, and interpret data. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the foundation in probability, statistics, and linear algebra that is necessary for this field. It will equip you with the tools to analyze data, build models, and make informed conclusions.
Financial Analyst
Financial Analyst
Financial Analysts use mathematical and analytical skills to evaluate the performance of companies, industries, and economies. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can help you build a strong foundation in these areas, providing you with the tools to analyze financial data, make projections, and provide recommendations to clients.
Investment Analyst
Investment Analyst
As an Investment Analyst, you will analyze financial data to provide recommendations on investment decisions. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can give you the mathematical and analytical foundation required to perform complex calculations and make informed decisions. By understanding calculus, linear algebra, and financial modeling, you will be prepared for the quantitative aspects of investment analysis.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the foundation in mathematics and problem-solving that is necessary for this field. It will equip you with the skills to analyze problems, design solutions, and implement them in software.
Teacher
Teacher
Mathematics teachers educate students in the principles and applications of mathematics. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course can provide you with the foundation in calculus, algebra, and linear algebra that is necessary for teaching these topics at the secondary or post-secondary level. It will equip you with the knowledge and skills to effectively teach students about these important mathematical concepts.
Data Analyst
Data Analyst
Data Analysts use mathematical and analytical skills to extract insights from data. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course may be useful for this role, as it will provide you with the foundation in calculus, linear algebra, and statistics that is necessary for understanding and analyzing data.
Consultant
Consultant
Consultants provide advice and guidance to businesses and organizations on a variety of topics. The Mathematics 1 Part 2: Integral calculus, algebra, and applications course may be useful for this role, as it will provide you with the analytical and problem-solving skills that are necessary for success in consulting.
For more career information including salaries, visit:
OpenCourser.com/course/qzzww4/mathematics
Reading list
We've selected 14 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
Mathematics 1 Part 2: Integral calculus, algebra, and applications.
This comprehensive textbook specifically tailored for economics students covers the mathematical concepts and techniques used in the field, including calculus, linear algebra, and optimization. It valuable resource for understanding the mathematical underpinnings of economics.
This comprehensive textbook provides a thorough grounding in the concepts and techniques of calculus, including the integration covered in the course. It is an excellent resource for building a strong foundation in the subject.
This widely-used textbook covers the fundamentals of linear algebra, including matrices, vectors, and linear equations. It valuable resource for understanding the linear algebra topics in the course and exploring them further.
This introductory textbook provides a clear and concise introduction to linear algebra, covering the fundamentals explored in the course. It valuable resource for gaining a deeper understanding of the subject.
This applied calculus textbook focuses on applications in various fields, including economics. It provides a practical perspective on the mathematical concepts covered in the course.
This advanced textbook explores optimization techniques used in economic theory, including constrained optimization. It provides a deeper understanding of the mathematical concepts covered in the course and their applications in economics.
Save
This foundational textbook in microeconomics provides insights into the profit maximization and constrained optimization concepts discussed in the course. It offers a real-world context for the mathematical techniques.
This specialized textbook covers the techniques used in financial modeling, including sequences, series, and financial modeling. It provides practical insights into the mathematical tools used in the financial industry.
This advanced textbook covers the mathematical foundations of financial models, including sequences, series, and financial modeling. It valuable resource for those interested in exploring these topics in greater depth.
This comprehensive econometrics textbook provides insights into the applications of mathematical techniques in economic analysis. It offers a valuable perspective on using mathematical tools to solve real-world economic problems.
This classic textbook covers a wide range of mathematical methods used in the physical sciences, including calculus, matrices, and differential equations. It provides a comprehensive overview of the mathematical tools used in various scientific disciplines.
This advanced linear algebra textbook provides a rigorous and comprehensive treatment of the subject. It covers topics that provide a deeper understanding of the linear algebra concepts explored in the course.
Save
This advanced calculus textbook provides a comprehensive treatment of the subject, including topics related to integration and differential equations. It valuable resource for students interested in a deeper understanding of the mathematical foundations of calculus.
This advanced textbook provides a comprehensive introduction to measure theory and integration theory. It covers topics that provide a theoretical foundation for the integration concepts explored in the course.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/qzzww4/mathematics
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Rating
4.6
Effort
12 to 15 hours per week for 5 weeks
Level
Introductory
Via
edX
Institution
The London School of Economics and Political Science
Instructor
Martin Anthony
Language
English
Transcript
English
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