How should I prepare myself for a proof-orientated linear algebra course?

In summary, the individual is seeking advice on how to prepare for a proof-orientated linear algebra course they will be taking in the fall. They have limited experience with proofs and have only taken calculus courses where proofs were not emphasized. They have purchased a textbook to study and are open to suggestions for other resources. It is recommended to practice with online sources and books such as Courant and Robbins or Spivak's calculus to gain experience with proofs before taking the course.
  • #1
opticaltempest
135
0
Hello all,

I am taking a linear algebra course at my university this fall. This course is used as a transition to more proof-orientated courses. From what I hear, this course is one where students generally do poorly if they lack the ability to construct proofs. I don't have much experience reading or constructing proofs. I have completed courses in Calculus I,II,III, and Differential Equations. However, these courses were the typical courses where proof-based material was omitted. How can I best prepare myself for a proof-orientated linear algebra class?

I purchased this textbook in order to study the first four chapters. I'm hoping it will help prepare me for writing proofs. Any suggestions?

http://vig.prenhall.com/catalog/academic/product/0,1144,0131481010-TOC,00.html"

https://www.amazon.com/dp/0131481010/?tag=pfamazon01-20Thanks
 
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  • #3
you might try working your way through courant and robbins, even for only a few pages. or spivaks calculus.
 

1. What is the best way to review my algebra skills before starting a proof-orientated linear algebra course?

The best way to review your algebra skills for a proof-orientated linear algebra course is to practice solving algebraic equations, simplify expressions, and familiarize yourself with basic algebraic concepts such as factoring, solving systems of equations, and working with matrices. You can also use online resources or textbooks to refresh your knowledge.

2. Are there any specific topics or concepts that I should focus on before starting a proof-orientated linear algebra course?

Some important topics and concepts to focus on before starting a proof-orientated linear algebra course include understanding the properties of matrices, matrix operations, solving systems of equations, and working with vectors and vector spaces. It is also helpful to have a strong understanding of basic algebraic principles and notation.

3. How important is it to have a strong foundation in calculus for a proof-orientated linear algebra course?

Having a strong foundation in calculus is not necessary for a proof-orientated linear algebra course. However, some concepts in linear algebra may involve calculus, such as computing eigenvalues and eigenvectors. It is helpful to have a basic understanding of calculus, but it is not a prerequisite for the course.

4. What resources are available to help me prepare for a proof-orientated linear algebra course?

There are many resources available to help you prepare for a proof-orientated linear algebra course. You can use online tutorials, practice problems, textbooks, and study groups to brush up on your skills and familiarize yourself with the course material. Your professor or teaching assistant may also provide study guides or review sessions.

5. Is it necessary to have prior experience with proofs before taking a proof-orientated linear algebra course?

No, it is not necessary to have prior experience with proofs before taking a proof-orientated linear algebra course. Your professor will likely provide an introduction to proofs and guide you through the process of writing and understanding mathematical proofs. However, having some familiarity with logical reasoning and mathematical notation can be beneficial.

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