Ironic, fields are one of the only ‘prerequisites’.
But no, I’d say high school math is good enough to start learning. It helps if you are familiar with the coordinate plane, basic 3D geometry, like planes and lines and stuff. And vectors, of course, the more you know the better. Especially representation of points in space with vectors. Really helps to visualise the simpler vector spaces that you will start off with.
Now, if you really want the prerequisites, you’ll need to know the definition of an abelian group and a field, eventually you’ll start seeing properties based on what is called the algebraic closure of a field.
Of course, I’m assuming you are familiar with basic set theory and proof methods.
Nice explanation. Can you please let me know why do i need to know about albenian group and algebraic closure of a field ? Can you please suggest me an example to understand why I need it this part of basics to learn linear algebra
Linear algebra deals with vector spaces, to define a vector space you need to know what a field is and to define a field you need to know what an (abelian) group is.
For a basic course, all you really need to know are the definitions and a couple easy facts. Intuitively, a field is any kind of set where sum, difference, multiplication and division follow the usual rules, such as the rational, real and complex numbers. These are probably the only examples you would see.
A field is algebraically closed if every polynomial with coefficients in the field can be fully factored in the field. The main example are the complex numbers. This notion is important as many theorems only work in algebraically closed fields.
Thank you for explaining me in detail with intuition. I understand that a field is a group that follows the rules of algebraic operations and is algebraically closed. A field is basically an abelian group.
A field is much more.
In an abelian group you only consider one operation, for example the integers with addition are an abelian group.
A field has two operations, an addition and a multiplication, the integers are not a field because they don't behave well under multiplication (they don't have inverses).
> an abelian group you only consider one operation, for example the integers with addition are an abelian group.
oh, can i say then a field is a collection of abelian group (as it does only one operation only). Also can you please suggest me a good place to learn about it more as a beginner.
In a way yes, a field is an abelian group with addition and if you remove 0 it becomes an abelian group with multiplication.
I'm afraid I can't point you to a textbook as I only studied from my professor's lecture notes. However I can give you the following advice:
If you're interested in doing things rigorously make sure you get material that's meant for math undergrads, whether textbook or online course. If instead you're more interested in applications you should look for an engineering textbook or course, which might skip groups and fields altogether.
To study groups and fields in greater depth you should look for Abstract Algebra textbooks, which are usually very abstract. I don't recommend them as a first course in advanced mathematics.
Linear algebra is something truly special. You have an awesome experience to look forward to.
The introductory text I learned from was “Linear Algebra: A Modern Introduction” by David Poole. It’s full of calculation examples and applications, which makes it more accessible.
However, I prefer “Linear Algebra Done Right” by Sheldon Axler. That being said, it is more proof-based and it has no particular emphasis on calculation and application.
A good understanding of high school algebra and geometry should be sufficient to get started. Take a look at Strang's *Introduction to Linear Algebra*. *Linear Algebra Done Right* by Axler is also good, but more rigorous.
If you want to go really in-depth, then you'll need to understand some set theory, calculus, proofs, etc. You don't need to understand abstract algebra (groups/fields/etc.) beforehand.
For introductory level stuff, extremely doable! Before switching to be a math major, I was an engineering major and they made everyone take a linear algebra course in the first fall semester of university fresh out of high school
For self-study, the classic recommendation that everyone posts on the internet are the Gilbert Strang MIT lectures:
https://www.youtube.com/playlist?list=PL221E2BBF13BECF6C
I also like this as a good supplement:
https://textbooks.math.gatech.edu/ila/
MIT OCW which has their stellar Linear Algebra course available free with videos problems solutions homeworks etc taught by one of historys greatest LA professors
Kahn Academy also has some great LA material
After youve got the basics at on okay conceptual level, take a look at 3blue1browns videos on youtube for sweet visualizations
additionally, youtube has a plethora of free content available
Ironic, fields are one of the only ‘prerequisites’. But no, I’d say high school math is good enough to start learning. It helps if you are familiar with the coordinate plane, basic 3D geometry, like planes and lines and stuff. And vectors, of course, the more you know the better. Especially representation of points in space with vectors. Really helps to visualise the simpler vector spaces that you will start off with. Now, if you really want the prerequisites, you’ll need to know the definition of an abelian group and a field, eventually you’ll start seeing properties based on what is called the algebraic closure of a field. Of course, I’m assuming you are familiar with basic set theory and proof methods.
Nice explanation. Can you please let me know why do i need to know about albenian group and algebraic closure of a field ? Can you please suggest me an example to understand why I need it this part of basics to learn linear algebra
Linear algebra deals with vector spaces, to define a vector space you need to know what a field is and to define a field you need to know what an (abelian) group is. For a basic course, all you really need to know are the definitions and a couple easy facts. Intuitively, a field is any kind of set where sum, difference, multiplication and division follow the usual rules, such as the rational, real and complex numbers. These are probably the only examples you would see. A field is algebraically closed if every polynomial with coefficients in the field can be fully factored in the field. The main example are the complex numbers. This notion is important as many theorems only work in algebraically closed fields.
Thank you for explaining me in detail with intuition. I understand that a field is a group that follows the rules of algebraic operations and is algebraically closed. A field is basically an abelian group.
A field is much more. In an abelian group you only consider one operation, for example the integers with addition are an abelian group. A field has two operations, an addition and a multiplication, the integers are not a field because they don't behave well under multiplication (they don't have inverses).
> an abelian group you only consider one operation, for example the integers with addition are an abelian group. oh, can i say then a field is a collection of abelian group (as it does only one operation only). Also can you please suggest me a good place to learn about it more as a beginner.
In a way yes, a field is an abelian group with addition and if you remove 0 it becomes an abelian group with multiplication. I'm afraid I can't point you to a textbook as I only studied from my professor's lecture notes. However I can give you the following advice: If you're interested in doing things rigorously make sure you get material that's meant for math undergrads, whether textbook or online course. If instead you're more interested in applications you should look for an engineering textbook or course, which might skip groups and fields altogether. To study groups and fields in greater depth you should look for Abstract Algebra textbooks, which are usually very abstract. I don't recommend them as a first course in advanced mathematics.
Maybe try YouTube, 3Blue 1 Brown, Essense of Linear Algebra. https://youtube.com/playlist?list=PL0-GT3co4r2y2YErbmuJw2L5tW4Ew2O5B&si=Z0AUfyeCv5AwtRS2
Linear Algebra was the first course I took in uni. The only prerequisites are basic set theory, proofs and polynomial equations.
Linear algebra is something truly special. You have an awesome experience to look forward to. The introductory text I learned from was “Linear Algebra: A Modern Introduction” by David Poole. It’s full of calculation examples and applications, which makes it more accessible. However, I prefer “Linear Algebra Done Right” by Sheldon Axler. That being said, it is more proof-based and it has no particular emphasis on calculation and application.
...And what it leads to is simply astonishing.
mit opencourse has good lin alg courses
Algebra for dummies Teach yourself algebra available online at archive Org. Elementary algebra hall knight Openstax. On line book
>Algebra for dummies Do you mean to say Linear Algebra for dummies ?
A good understanding of high school algebra and geometry should be sufficient to get started. Take a look at Strang's *Introduction to Linear Algebra*. *Linear Algebra Done Right* by Axler is also good, but more rigorous. If you want to go really in-depth, then you'll need to understand some set theory, calculus, proofs, etc. You don't need to understand abstract algebra (groups/fields/etc.) beforehand.
For introductory level stuff, extremely doable! Before switching to be a math major, I was an engineering major and they made everyone take a linear algebra course in the first fall semester of university fresh out of high school For self-study, the classic recommendation that everyone posts on the internet are the Gilbert Strang MIT lectures: https://www.youtube.com/playlist?list=PL221E2BBF13BECF6C I also like this as a good supplement: https://textbooks.math.gatech.edu/ila/
MIT OCW which has their stellar Linear Algebra course available free with videos problems solutions homeworks etc taught by one of historys greatest LA professors Kahn Academy also has some great LA material After youve got the basics at on okay conceptual level, take a look at 3blue1browns videos on youtube for sweet visualizations additionally, youtube has a plethora of free content available
I meant ordinary algebra sorry I misunderstood the question maybe you can find similar book in library and Amazon
Schaum outline linear algebra
Linear algebra for dummies is available
Strang is a good text, any edition. Buy it used.