Matematik Exercise

[Rene Seiler]

Discrete Mathematics: An Open Introduction is a free, open source textbook appropriate for a first or second year undergraduate course for math and computer science majors. The book is especially well-suited for courses that incorporate inquiry-based learning. Since Spring 2013, the book has been used as the primary textbook or a supplemental resource at more than 200 colleges and universities around the world (see the partial adoptions list). The text is endorsed by the American Institute of Mathematics' Open Textbook Initiative and is well reviewed on the Open Textbook Library.

This 3rd edition brings many improvements, including nearly 100 new exercises (including many interactive exercises providing instant feedback), a new section on trees in the graph theory chapter, and improved exposition throughout. Previous editions will continue to be available indefinitely. A few times a year, the text is updated with a new "printing" to correct errors. See the errata list for more information.

Online homework sets are available through Runestone Academy (free), Edfinity (inexpensive) or as WeBWorK sets from the author (the WeBWorK exercises are available in the Contrib folder of the OPL as well).

Please contact the author with feedback and suggestions, or if you are decide to use the book in a course you are teaching. You can also easily submit feedback about an error or typo by creating a GitHub issue.

The entire book is available for free as an interactive online ebook. This should work well on all screen sizes, including smart phones, and work will with screen readers for visually impaired students. Hints and solutions to examples and exercises are hidden but easily revealed by clicking on their links. Some exercises also allow you to enter and check your work, so you can try multiple times without spoiling the answer.

For offline use, a free pdf version, suitable for reading on a tablet or computer, is available for download. This should be searchable and easy to navigate using embedded links. Hints and solutions (when available) can be accessed by clicking on the exercise number, and clicking on the number of the hint or solution will bring you back to the exercise.

If you prefer a physical copy, an inexpensive print version of the text is available on Amazon. This should be cheaper than printing the entire book and binding it yourself. Page numbers match the pdf version. There is also a cheap Kindle version available; it works great on Android tablets; unfortunately it seems the math does not render well on Amazon's e-ink readers.

There are a number of videos instructors have made for classes they taught using the book. Check out the playlists below. If you make videos or know of others, please share them.

• Mathematical Visual Proofs. Beautifully animated videos illustrating ideas from the book.
• Dr. Trevor Bazett's Course. A complete course that uses the textbook as a basis for the videos.

If you are using the book in a class you are teaching, instructor resources are available by request. Just contact the author. You can also request WeBWorK homework sets if you have access to a WeBWorK server.

The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proofs" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this. Originally designed to support future math teachers, the text has a friendly and informal tone, and puts an emphasis on understanding the included concepts, rather than simply memorizing procedures. The book has also been successfully used in courses catering to computer science students, who also benefit from the deeper understanding it promotes.

Four main topics are covered: counting, sequences, logic, and graph theory. Along the way, proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs. An introductory chapter covering mathematical statements, sets, and functions helps students gain familiarity with the language of mathematics, and two additional topics (generating functions and number theory) are also included.

Oscar Levin is a professor at the University of Northern Colorado. He has taught mathematics and computer science at the college level for over 15 years and received multiple teaching awards. He received his Ph.D. in mathematical logic from the University of Connecticut in 2009.

Discrete Mathematics: An Open Introduction by Oscar Levin is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License. You are free to download, use, print, and even sell this work as you wish to. You can also modify the text as much as you like (create a custom edition for your students, for example), as long as you attribute the parts of the text you use to the author.

And then the big one, money. Financial literacy is an incredibly important skill for adults to master. It can help you budget, save and even help you make big decisions like changing careers or buying a home.

Mathematical knowledge may even be connected to many other not-so-obvious benefits. A strong foundation in math can translate into increased understanding and regulation of your emotions, improved memory and better problem-solving skills.

Solving math problems and improving our math skills gives our brain a good workout. And it improves our cognitive skills over time. Many studies have shown that routinely practicing math keeps our brain healthy and functioning well.

At first, classic math problems like Johnny bringing home 42 watermelons and returning 13 of them can just seem a silly exercise. But all those math word problems our children solve really do improve their problem solving skills. Word problems teach kids how to pull out the important information and then manipulate it to find a solution.

Later on, complex life problems take the place of workbooks, but problem-solving still happens the same way. When students understand algorithms and problems more deeply, they can decode the facts and more easily solve the issue. Real-life solutions are found with math and logic.

This is because math problems often require us to bend our thinking and approach problems in more than one way. The first process we try might not work. We need flexibility and creativity to think of new pathways to the solution. And just like anything else, this way of thinking is strengthened with practice.

But many other professionals use math skills every day to complete their jobs. CEOs use math to analyze financials. Mailmen use it to calculate how long it will take them to walk their new route. Graphic designers use math to figure out the appropriate scale and proportions in their designs.

Math can certainly open up a lot of opportunities for many of us. But did you know that careers which heavily use math are going to be among the fastest-growing jobs by the time kids today start their careers? These jobs include:

The parts of the brain used to solve math problems seem to work together with the parts of the brain that regulate emotions. This suggests that math practice can actually help us cope with difficult situations. In these studies, the better someone was with numerical calculations, the better they were at regulating fear and anger. Strong math skills may even be able to help treat anxiety and depression.

As they age into adulthood, It will benefit your child to understand how loans and interest work before purchasing a house or car. They should fully grasp profits and losses before investing in the stock market. And they will likely need to evaluate job salaries and benefits before choosing their first job.

These are words heard often from our toddlers. This phrase is a marker of growth, and a point of pride. But as your child moves into elementary school, you may not hear these words as often or with as much confidence as before.

Sometimes the pace of class moves a bit faster than your child can keep up with. Or the concepts are just too abstract and difficult for them to wrap their mind around in one lesson. Some math ideas simply take more time to learn.

Sometimes, all your child needs is a little more practice. But this can be easier said than done. You can help by providing them with plenty of support and encouragement to help them get that practice time in.

Prodigy Math is a game-based, online learning platform that makes learning math fun for kids. As kids play and explore a safe, virtual world filled with fun characters and pets to collect, they'll answer math questions. These questions are curriculum-aligned and powered by an adaptive algorithm that can help them master math skills more quickly.

Want to play an even bigger role in helping your child master math? Try our optional Math Memberships for extra in-game content for your child to enjoy and get amazing parent tools like the ability to set in-game goals and rewards for them to achieve.

Our Math course builds on what makes learning with Duolingo so delightful and engaging: fun animations, interactive exercises, and a world of characters cheering you along the way! We have two options for new learners: beginner math, which covers foundational topics, or intermediate math, which enhances everyday skills with more challenging exercises.

Each of our exercises are uniquely engineered for the content they teach. One way we do this is by having learners manipulate virtual tools, like the clock below. Having learners interact with these tools allows them to focus on the most important mathematical aspects of the objects and deepens their understanding of the underlying concepts. For example, in a clock challenge, we present a simplified version of a clock with the hands set arbitrarily. Then learners can move a minute or hour hand and watch how the other hand moves accordingly, solidifying their understanding of the relationship between hours and minutes. And this is only a fraction of the fun exercises we've developed! ?

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