Upper Level Algebra Q&A: Get Expert Help and Learn from Real-World Examples

Recent questions in Upper level algebra
College algebraOpen question
Jenna AusmussenJenna Ausmussen2022-10-25

College algebraOpen question
Charkesia MaddoxCharkesia Maddox2022-08-29

College algebraAnswered question
Feranmimakun6 Feranmimakun6 2022-08-25

College algebraAnswered question
Vicucyxycj Vicucyxycj 2022-07-17

College algebraAnswered question
ScommaMaruj ScommaMaruj 2022-07-08

I am from a non-mathematics background but the course that I am taking in probability class is built on measure theory. I found many theorems stated in the book hard to comprehend and I think that's partly due to my insufficient maths background. I am self-learning real analysis currently and think it may be equally important to systematically learn abstract algebra if I really want to know the logic behind the probability class I am currently taking.
I find myself completely lost proceeding to the following section of the text.

"Let R be a relation, A a mathematical object, and x a letter (i.e., a "totally indeterminate" mathematical object). In the assembly of letters and fundamental signs which constitutes the relation R, replace the letter x wherever it occurs by the assembly A. One of the criteria for forming relations is that the assembly so obtained is again a relation, which is denoted ( ) by the notation
( A x ) R
and is called the relation obtained by substituting A for x in R, or by giving x the value A in R. The mathematical object A is said to satisfy the relation R if the relation ( A x ) R is true. It goes without saying that if the letter x does not appear at all in the assembly R, then the relation ( A x ) R is just R, and in this case to say that A satisfies R means that R is true."

However, I do appreciate the textbook that is self-contained and appreciate the author devoted to mathematical reasoning so rigorously at the beginning of the chapter. I tried to find some textbook about mathematical logic but they are either too abstract or not thorough enough that seems to start from the most fundamental (i.e. from axiom and the most basic rule).
I have read relevant posts on the subject I am asking but can't decide the material right for me. I am wondering if there are any materials or textbooks that introduce mathematical logic rigorously and serve as a supplementary text for me to understand the first chapter of the book? If there really isn't any textbook that is not too abstract but rigorous enough, I am wondering if there are any other textbooks on abstract algebra that start from mathematical logic and build the whole system from the scratch?

As a rule, when there is a task that relates to upper-level Algebra, it is usually met among mechanical or electrical engineers, architects, and students dealing with statistical calculations. The questions that have been posted below explore several concepts and explain why the problems in upper-level Algebra occur. Speaking of college algebra answers online, one should take a closer look at calculations that have been based on real-life cases. It will help to determine the solution. See more than one question as you do. See our college algebra examples with answers to find your ultimate guidance.