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xsqueetzzz
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I'm taking both in the fall, what should I review over the summer to prep up for this?
How Should I Prepare for Calculus III and Modern Algebra?
- Thread starter xsqueetzzz
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In summary, if you are having trouble with algebra, I would recommend starting with a course like Modern Geometry, Junior level Linear Algebra, or Elementary Number Theory. These will prepare you for the more abstract proofs found in Algebra. Additionally, I would recommend picking up a copy of "Pinter" and "Marsden's free Calc III book" to get a feel for what the class will be like.
- #2
YAHA
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Calculus II for Calculus III 
- #3
- 22,183
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Hi xsqueetzzz!
Be sure to be acquainted with proofs before you embark in algebra. It'll make your life a whole lot easier!
Be sure to be acquainted with proofs before you embark in algebra. It'll make your life a whole lot easier!
- #4
hitmeoff
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micromass said:Hi xsqueetzzz!
Be sure to be acquainted with proofs before you embark in algebra. It'll make your life a whole lot easier!
Agreed. At my school, the Algebra sequence is probably the toughest sequence we have, and some of the professor that teach it will take no prisoners when it comes to level they expect you to perform.
So from my perspective, I personally think you are better off starting your "Junior Level" math course with something like Modern Geometry, Junior level Linear Algebra or even Elementary Number Theory. Usually, these three will serve as a nice bridge between computational math and abstract, proof based math.
Of course, in your school, Number Theory or LA or even Modern Geo maybe be deadly classes and Algebra may be taken more lightly! So it really depends. I would definitely look over your Elementary Linear Algebra book (you know the freshman/sophomore level LA), and practice some of the "Proof" problems. That should get you started on thinking more abstractly.
- #5
Chaostamer
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Honestly, it might benefit you to do some independent study in number theory, both because you'll get more practice with proofs and because number theory knowledge makes algebra easier--or so I've been told. "Elementary Number Theory" by Jones and Jones is an excellent book in that regard. It's really well written and has a comprehensive solutions key in the back, so it's ideal for self-study. Plus, it's pretty cheap. I'd highly recommend it if you want some accessible proof practice.
- #6
Sankaku
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It is a very good recommendation from micromass to make sure you are comfortable with proofs.
If that is covered, pick up a copy of Pinter:
https://www.amazon.com/dp/0486474178/?tag=pfamazon01-20
It is cheap, an easy read, and will introduce you to the basic concepts of algebra.
You can glance through Marsden's free Calc III book to get an idea of what that will be like.
http://www.e-booksdirectory.com/details.php?ebook=1564
If that is covered, pick up a copy of Pinter:
https://www.amazon.com/dp/0486474178/?tag=pfamazon01-20
It is cheap, an easy read, and will introduce you to the basic concepts of algebra.
You can glance through Marsden's free Calc III book to get an idea of what that will be like.
http://www.e-booksdirectory.com/details.php?ebook=1564
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Related to How Should I Prepare for Calculus III and Modern Algebra?
What is Calculus III?
Calculus III, also known as Multivariable Calculus, is a branch of mathematics that deals with the study of functions of more than one variable. It extends the concepts of Calculus I and II, which focus on functions of a single variable, to functions of two or more variables. It involves topics such as partial derivatives, multiple integrals, and vector calculus.
What is Modern Algebra?
Modern Algebra, also known as Abstract Algebra, is a branch of mathematics that studies algebraic structures such as groups, rings, and fields. It generalizes the algebraic concepts of numbers and operations to more abstract settings, allowing for the study of structures with different properties and operations. Modern Algebra has applications in many fields such as cryptography, coding theory, and physics.
What are the main topics covered in Calculus III?
The main topics covered in Calculus III include partial derivatives, multiple integrals, vector calculus, and line and surface integrals. Other topics that may be covered include vector fields, Green's theorem, Stoke's theorem, and the Divergence theorem. These topics are essential for understanding multivariable functions and their applications in various fields.
Why is Calculus III important?
Calculus III is important because it provides a deeper understanding of functions of multiple variables, which are found in many real-world applications. It is also a crucial step in many STEM fields, such as physics, engineering, and economics, as it lays the foundation for advanced courses in these areas. Additionally, the problem-solving skills and critical thinking developed in Calculus III are valuable in many areas of life.
What are the prerequisites for studying Calculus III & Modern Algebra?
The prerequisites for studying Calculus III & Modern Algebra vary depending on the institution and program. However, typically, a strong understanding of Calculus I and II is required, as well as a good grasp of algebra, trigonometry, and geometry. Some programs may also require a background in linear algebra and differential equations. It is important to check the specific prerequisites for the course or program you are interested in taking.
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