Unknown capital letters

[ahmedcrow]

Hello everyone, my education level is the secondary school, I finished it in 1999, I tried to fresh my memory and studying math again with myself, our books are in Arabic, I didn't study mathematics in English before, I read in the secondary school math book about linear programming, I liked it and I wanted to know more, so I searched in web for more sources and found this English source "LINEAR PROGRAMMING
A Concise Introduction
Thomas S. Ferguson"

I found this problem and I didn't understand well what these capital letters mean, I don't know this way in secondary school books or it may be something of high mathematics, I marked these letters with red.

 

[tkhunny]

Hello everyone, my education level is the secondary school, I finished it in 1999, I tried to fresh my memory and studying math again with myself, our books are in Arabic, I didn't study mathematics in English before, I read in the secondary school math book about linear programming, I liked it and I wanted to know more, so I searched in web for more sources and found this English source "LINEAR PROGRAMMING
A Concise Introduction
Thomas S. Ferguson"

I found this problem and I didn't understand well what these capital letters mean, I don't know this way in secondary school books or it may be something of high mathematics, I marked these letters with red.

You'll have to find a way to communicate that does not include links to hosting sites with ads and pornography.

 

[mmm4444bot]

Please read the forum guidelines, before posting again. Thank you. :cool:

 

[Dr.Peterson]

Hello everyone, my education level is the secondary school, I finished it in 1999, I tried to fresh my memory and studying math again with myself, our books are in Arabic, I didn't study mathematics in English before, I read in the secondary school math book about linear programming, I liked it and I wanted to know more, so I searched in web for more sources and found this English source "LINEAR PROGRAMMING
A Concise Introduction
Thomas S. Ferguson"

I found this problem and I didn't understand well what these capital letters mean, I don't know this way in secondary school books or it may be something of high mathematics, I marked these letters with red.

Perhaps this is a copy of the book you are using: https://www.math.ucla.edu/~tom/LP.pdf .

If so, and if you are unable to upload a picture of your problem to our site, you might just tell us the page and problem number, quote the problem, and tell us in words what you are confused about. In fact, if you had typed in the problem and what the letters are that you are asking about, I might be giving you an answer already!

 

[Dr.Peterson]

Since the source I found is not very long, I skimmed through it and didn't see many capital letters you might be referring to. Subscripted capital letters are used for variables in examples; capital letters (usually A) are used for matrices; and T indicates a transpose.

If you simply haven't learned about matrices, then this is not the appropriate source for you to be using! You will need more introductory material, rather than a quick review for advanced students.

 

[ahmedcrow]

Perhaps this is a copy of the book you are using: https://www.math.ucla.edu/~tom/LP.pdf .

If so, and if you are unable to upload a picture of your problem to our site, you might just tell us the page and problem number, quote the problem, and tell us in words what you are confused about. In fact, if you had typed in the problem and what the letters are that you are asking about, I might be giving you an answer already!

Yes, it's the book, page 5, example 1 "The diet problem", the capital letters F and N. For now I'm trying to study more linear programming but this book has advanced ways more than I already know of secondary school math, but if I found that I can't continue, what're the basic materials that can help me to understand this advanced mathematics.

 

[mmm4444bot]

Those symbols are subscripted. Here's a quick explanation.

The symbol A₄ has a subscript. The subscript is 4.

We use subscripts to distinguish between different members of a set.

Set A = {2, 4, 6, 8, 10}

A₄ is the fourth element in the set. Therefore, A₄ = 8

If I didn't know any of the five values in set A, I could still define the set:

A = {A₁, A₂, A₃, A₄, A₅}

I could also write A_i where the subscript i is used as an index. For example, if I know that 6 is an element in set A, but I don't know its position, I can write A_i=6

In fact, I could talk about set A even if I didn't know how many elements it has. I would choose a symbol for the number of elements: n

A_i = {A₁, … A_n} where the index i goes from 1 to n

Subscripts provide a way to communicate symbolically. :cool:

 

[mmm4444bot]

… if I [find] that I can't continue, what're the basic materials that can help me to understand …

It's hard for me to know (without any meetings) what helps you to understand. (I have assumed that you already refreshed your memory on the basics you knew in 1999.)

We could deal with roadblocks on a case-by-case basis. When you see something that you cannot understand, you can ask about it specifically. We can help you get around the roadblocks.

Later, if you decide you don't like that book, it would help to know why; we might be able to look for something different.

You're free to study at your own pace, yes? :cool:

 

[Dr.Peterson]

Yes, it's the book, page 5, example 1 "The diet problem", the capital letters F and N. For now I'm trying to study more linear programming but this book has advanced ways more than I already know of secondary school math, but if I found that I can't continue, what're the basic materials that can help me to understand this advanced mathematics.

Those are just variable names being introduced -- no advanced math yet! It says,

There are m different types of food, F₁,...,F_m, that supply varying quantities of the n nutrients, N₁,...,N_n, that are essential to good health.
​

F₁ represents the name of the first of m types of food, etc. N₁ represents the name of the first of n nutrients.

So when it says, "Let c_j be the minimum daily requirement of nutrient, N_j.", that means that, for example, c₁ is a variable representing the MDR of the first nutrient.

The fact that you struggle here suggests that the initial problem is the style -- this is written at a level that people accustomed to reading advanced math will be familiar with, not at a high school (much less forgotten high school!) level.

 

[ahmedcrow]

It's hard for me to know (without any meetings) what helps you to understand. (I have assumed that you already refreshed your memory on the basics you knew in 1999.)

We could deal with roadblocks on a case-by-case basis. When you see something that you cannot understand, you can ask about it specifically. We can help you get around the roadblocks.

Later, if you decide you don't like that book, it would help to know why; we might be able to look for something different.

You're free to study at your own pace, yes? :cool:

We've in secondary Egyptians schools 3 grades, 3 years, class 1, class 2, class 3, and there're 2 section, the scientific section or literary one which doesn't study science or much of math, in my days there're 3 sections, scientific, literary and math, I chose math section, the choosing will be in the second class of high school, the second year.

Shortly, we study some of algebra, trigonometry, dynamic, static, solid geometry, may be analytic geometry, some of statistics, calculus.

What I'm planning too is that I want to be able to read and understand the high mathematics books, I want the high mathematics but I don't know the way, all what I know is to refresh my memory with the high school books, I started now with algebra.

Also, I hope you tell me how to type the mathematics symbols and notation in the forum, I don't know how to do it with computers to be able to type problems I can't solve in the forum.

 

[mmm4444bot]

… I want to be able to read and understand the high mathematics books, I want the high mathematics but I don't know the way, all what I know is to refresh my memory with the high school books, I started now with algebra.

I think your plan to refresh your memory starting with algebra is good. We learn higher mathematics by first having a thorough understanding of what comes before it.

There are several free algebra courses and textbooks on the Internet. There are many more video explanations and lesson pages for specific algebra concepts. You can use Google to find them.

… I hope you tell me how to type the mathematics symbols and notation in the forum …

Did you see post #3 ?

Those guidelines provide information on three different ways to type math in the forum. :cool:

If you're stuck on something specific, start a new thread and ask us about it. (You can put technical questions about the forum on the Administrative Issues board.) We will help you get around any roadblocks.

 

[ahmedcrow]

Thank you mmm4444bot and doctor Peter, I think that I'll continue reading this book later, I think that I need to prepare myself for higher mathematics first.