Statistics-lab™可以为您提供luc.edu MATH355 abstract algebra抽象代数课程的代写代考和辅导服务！
MATH355 abstract algebra课程简介
Algebra gives us tools to solve equations. The integers, the rationals, and the real numbers have special properties which make algebra work according to the circumstances. In this course, we generalize algebraic processes and the sets upon which they operate in order to better understand, theoretically, when equations can and cannot be solved. We define and study abstract algebraic structures such as groups, rings, and fields, as well as the concepts of factor group, quotient ring, homomorphism, isomorphism, and various types of field extensions. This course introduces students to abstract rigorous mathematics.
PREREQUISITES
The course will cover roughly chapters $1-5$ and 7 of the text. A list of topics is below.
- The integers and other familiar sets of numbers
- $\mathrm{N}, \mathrm{Z}, \mathrm{Q}, \mathrm{R}, \mathrm{C}$ (Should we include 0 in $\mathrm{N}$ ?)
- The well-ordering principle and induction
- Divisibility
- The division algorithm
- greatest common divisors. Euclidian algorithm?
- Bezout’s identity
- Least common multiples
- Prime numbers
- Euclid’s lemma
- Fundamental theorem of arithmetic
- Infinitely many primes
- Functions, Domain, Range, etc.
- Equivalence Relations
- Partitions
- Kernels of functions
- Well-definededness
MATH355 abstract algebra HELP（EXAM HELP， ONLINE TUTOR）
Exercise 1. Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not $90^{\circ}$ ). Describe all the symmetries of the rhombus. Write down the Cayley table for the group of symmetries.
Exercise 2 . Consider the set $\mathbb{Z}$ and the binary operation $\star$ on $\mathbb{Z}$ given by
$$
x \star y=x+x y .
$$
Does this operation make $\mathbb{Z}$ a group? Justify your answer.
Textbooks
• An Introduction to Stochastic Modeling, Fourth Edition by Pinsky and Karlin (freely
available through the university library here)
• Essentials of Stochastic Processes, Third Edition by Durrett (freely available through
the university library here)
To reiterate, the textbooks are freely available through the university library. Note that
you must be connected to the university Wi-Fi or VPN to access the ebooks from the library
links. Furthermore, the library links take some time to populate, so do not be alarmed if
the webpage looks bare for a few seconds.
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