 # Monash University Advanced Mathematics Course Details

Powerful Essays
1397 Words Grammar Plagiarism  Writing  Score Monash University Advanced Mathematics Course Details MONASH UNIVERSITY FOUNDATION YEAR

1. INTRODUCTION

A student taking this course must also be concurrently enrolled in (or previously studied) MUFY Mathematics Part A as many of the topics in MUFY Advanced Mathematics require an understanding of the concepts in MUFY Mathematics Part A.

2. COURSE OBJECTIVES

Advanced Mathematics is designed to prepare students who wish to take tertiary courses with a high mathematical content, or which use a considerable amount of mathematical reasoning. In Part A, students study matrices, complex numbers, vectors, trigonometric functions and differentiation techniques. In Part B the topics covered are integration techniques and applications of definite integrals, differential equations and kinematics.

3. COURSE CONTENT

Semester A: 1. Matrices & Linear Algebra

The concept of a matrix; matrix algebra, including addition, subtraction, and multiplication of matrices, and multiplication of a matrix by a scalar. The conditions necessary for the sum or product of matrices to exist.

The unit matrix, I; the meaning of the inverse, A-1, of a matrix A; the fact that AA-1 = A-1A = I.

Determinants; the determinant of a 2 x 2 matrix; the inverse of a 2 x 2 matrix. The use of matrices to solve systems of two equations in two unknowns.

Singular matrices; the fact that, if a matrix is singular, the equations it represents must be either dependent or inconsistent.

2. Complex Numbers

Algebraic form [pic] where [pic] and where x, y are real numbers. The terminology complex plane. The real part, and imaginary part, of z defined. Addition and subtraction defined algebraically. Multiplication based on the definition[pic].

The complex conjugate [pic] of [pic]. Property [pic]. Modulus of z. Division by complex numbers.

Polar form for non-zero z; arguments [pic] of z.

## You May Also Find These Documents Helpful

• Satisfactory Essays

A complex number is an expression in the form: a + bi where a and b are real numbers. The symbol i is defined as √ 1. a is the real part of the complex number, and b is the complex part of the complex number. If a complex number has real part as a = 0, then it is called a pure imaginary number. All real numbers can be expressed as complex numbers with complex part b = 0. -5 + 2i 3i 10 real part –5; imaginary part 2 real part 0; imaginary part 3 real part 10; imaginary part 0 complex number pure imaginary number real number…

• 357 Words
• 2 Pages
Satisfactory Essays
• Satisfactory Essays

A. Number Sense only deals with small matrices, usually 2 x 2 matrices. This page will look at 3 ways of manipulating matrices: Multiplying Matrices, Inverses, and Determinants. B. Multiplying Matrices 1. Unlike general multiplication, matrix multiplication is not commutative. Multiplying A x B and B x A will give different results. 2. The following will show how to multiply two 2x2 matrices:…

• 320 Words
• 2 Pages
Satisfactory Essays
• Good Essays

| a branch of mathematics that deals with the measurement, properties, and relationships of points, lines, angles, surfaces, and solids…

• 1391 Words
• 6 Pages
Good Essays
• Good Essays

The basic algebraic properties of the real numbers can be expressed in terms of the two fundamental operations of addition and multiplication.…

• 477 Words
• 2 Pages
Good Essays
• Good Essays

First unit: Sets. In this unit the fundamental concepts of the theory of sets is addressed to provide the tools and the language of operation for subsequent units.…

• 1481 Words
• 6 Pages
Good Essays
• Better Essays

* a major branch of mathematics which studies relations and operations. It's sometimes called abstract algebra, or "modern algebra" to distinguish it from elementary algebra.…

• 2220 Words
• 9 Pages
Better Essays
• Good Essays

Understanding math concepts is critical in our world today. Math is used daily by nearly everyone, from lay persons to highly degreed professionals. Situations in which math is used vary from simply balancing a checkbook or calculating the amount of change due from a store transaction all the way to making blueprints for an office building or house and the construction of those buildings. Understanding how to solve math problems becomes easier as one learns math terminology. Below is a list of many common math terms and their definitions.…

• 1756 Words
• 8 Pages
Good Essays
• Good Essays

8. Addition corresponds to moving to the right on the number line, whereas subtraction corresponds to moving to the left. Multiplication corresponds to making jumps of equal distance stating from zero.…

• 2796 Words
• 12 Pages
Good Essays
• Good Essays

The mathematical statements that describe relationships are expressed using algebraic terms, expressions, or equations (mathematical statements containing letters or symbols to represent numbers). Before we use algebra to find information about these kinds of relationships, it is important to first cover some basic terminology. In this unit we will first define terms, expressions, and equations. In the remaining units in this book we will review how to work with algebraic expressions, solve equations, and how to construct algebraic equations that describe a relationship. We will also introduce the notation used in algebra as we move through this unit. The numerical part of the term, or the number factor of the term, is what we refer to as the numerical coefficient. This numerical coefficient will take on the sign of the operation in front of it. The term above contains a numerical coefficient, which includes the arithmetic sign, and a variable or variables. In this case the numerical coefficient is –3 and the variables in the term are a and x. Terms such as xz may not appear to have a numerical coefficient, but they do. The numerical coefficient is 1, which is assumed.…

• 594 Words
• 2 Pages
Good Essays
• Powerful Essays

The syllabus has been designed to allow Centres flexibility to construct Mathematics courses appropriate to their…

• 8222 Words
• 33 Pages
Powerful Essays
• Good Essays

This may be thought of as a function which associates each square matrix with a unique number (real or complex). If M is the set of square matrices, K is the set of numbers (real or complex) and f : M → K is defined by f (A) = k, where A ∈ M and k ∈ K, then f (A) is called the determinant of A. It is also denoted by | A | or det A or Δ.…

• 10481 Words
• 42 Pages
Good Essays
• Satisfactory Essays

A one dimensional array is a variable that holds more than one index value such as car [ 13 ]. A Two dimensional array will hold two different index values such as…

• 290 Words
• 2 Pages
Satisfactory Essays
• Good Essays

In arithmetic we use only positive numbers and zero, but with algebra, we use both positive and negative numbers. The numbers we use in algebra are called the “real numbers” or integers {… , -3, -2, -1, 0, 1, 2, 3…}. In this paper I am going to explain the properties of real numbers using three examples. I will also be explaining how to solve these examples step by step, all while discussing why these properties are so important to begin with. The properties of real numbers are the commutative, associative, identity, and additive inverse properties of addition, distributive law, and the commutative, associative, identity, and the multiplicative inverse (reciprocal) of multiplication.…

• 656 Words
• 3 Pages
Good Essays
• Good Essays

A set is a collection of objects. The objects in a set are called the elements of the set. A set of numbers is simply a listing, within braces {}. For example, the set of numbers used for counting can be represented as S = {1, 2, 3, 4, 5, . . .}. The braces…

• 1254 Words
• 6 Pages
Good Essays
• Good Essays

x(10-x)=40, finding the answer to be 5 plus or minus √-15. Although he found that this was the answer, he greatly disliked imaginary numbers. He said that work with them would be, “as subtle as it would be useless”, and referred to working with them as “mental torture.” For a while, most people agreed with him. Later, in 1637, Rene Descartes came up with the standard form for complex numbers, which is a+bi. However, he didn’t like complex numbers either. He assumed that if they were involved, you couldn’t solve the problem. Lastly, he came up with the term “imaginary”, although he meant it to be negative. Issac Newton agreed with Descartes, and Albert Girad even went as far as to call these, “solutions impossible”. Although these people didn’t enjoy the thought of imaginary numbers, they couldn’t stop other mathematicians from believing that i might exist. (The History of Complex Numbers)…

• 641 Words
• 3 Pages
Good Essays