# First-year Mathematics and Statistics

Students intending to continue to level-2 (second-year) mathematics and statistics should take one of the four first-year mathematics and statistics pathways below. Which pathway(s) you can take depends on the level of mathematics that you completed at school and on your grades.

Completing one of these pathways satisfies the prerequisites for level-2 mathematics and statistics subjects.

The information below is intended for students commencing in semester 1. Students commencing mid-year are recommended to seek individual course advice.

## MAST10005 Calculus 1 Stream

### For students who completed VCE Mathematical Methods 3/4 but not VCE Specialist Mathematics 3/4, or achieved a VCE Specialist Mathematics 3/4 study score ≤ 29, or equivalent

Semester 1 | MAST10005 Calculus 1 |

Semester 2 | MAST10006 Calculus 2 |

Semester 2 or summer semester | MAST10007 Linear Algebra |

## Standard Stream

### For students with a study score ≥ 29 in VCE Specialist Mathematics 3/4 or equivalent

Our flagship first-year subjects cover the essential material with a focus on computation and applications. They are perfect for students who need to know mathematics in their chosen major or who want to broaden their education.

Semester 1 | MAST10006 Calculus 2 |

Semester 2 | MAST10007 Linear Algebra |

Bachelor of Science students in this stream can also take **MAST10010 Data Analysis 1** in semester 2 if they wish.

## Advanced Stream

### For students with a study score ≥ 36 in VCE Specialist Mathematics 3/4 or equivalent

The advanced stream is for students who want to understand the core first-year material in greater depth than would be possible in MAST10006/10007 or MAST10008/10009. This stream features more emphasis on mathematical proof, formal logic and communication than the accelerated or standard streams. It is designed for strong students interested in the beauty of formal mathematics, particularly those who intend to study higher level mathematics, statistics, physics and mathematical physics.

Semester 1 | MAST10022 Linear Algebra: Advanced |

Semester 2 | MAST10021 Calculus 2: Advanced |

Bachelor of Science students in this stream can also take **MAST10010 Data Analysis 1** in semester 2 if they wish.

## Accelerated Stream

### For students with a study score ≥ 38 in VCE Specialist Mathematics 3/4 or equivalent

The accelerated stream is for strong students who want to quickly cover the core first-year mathematics material as well as the equivalent of a second-year subject MAST20026 Real Analysis in two semesters. This rapid treatment also has more emphasis on mathematical proof than MAST10006 and MAST10007. This stream is highly recommended for Bachelor of Commerce students looking to major in Actuarial Studies.

Semester 1 | MAST10008 Accelerated Mathematics 1 |

Semester 2 | MAST10009 Accelerated Mathematics 2 |

Bachelor of Science students in this stream can also take **MAST10010 Data Analysis 1** in semester 2 if they wish.

Students with a Specialist Mathematics 3/4 study score of 35-37 may apply to sit the Advanced Placement Test to seek entry to the accelerated stream. Information about the Advanced Placement Test is available here.

The following subjects may be relevant to some students.

### MAST10010 Data Analysis 1

This subject lays the foundations for an understanding of the fundamental concepts of probability and statistics required for data analysis. Students should develop expertise in some of the statistical techniques commonly used in the design and analysis of experiments, and will gain experience in the use of a major statistical computing package.

*Recommended for students of biosciences and psychology, and those wishing to gain some knowledge of statistics.*

### MAST10012 Introduction to Mathematics

Students will strengthen and develop algebraic and conceptual skills, building a firm mathematical base for MAST10005 Calculus 1.

*Recommended for Design, Arts and Music students who did not complete VCE Mathematical Methods 3/4 or equivalent who are wishing to strengthen their mathematics and statistics skills or seeking a pathway to MAST10005 Calculus 1. This subject is not available to Science, Biomedicine or Commerce students, or to students with a study score of at least 25 in VCE Mathematical Methods 3/4 or equivalent.*

### MAST10020 Magic, Music, and Mathematics

Mathematics appears all around us in the world. While the uses of mathematics in areas such as finance, engineering and science are well known, it is less obvious how mathematical concepts and structures arise in entertainment, the arts and indeed in almost every field of human endeavour. In this subject we will develop the tools to appreciate and examine how mathematical concepts and structures arise in many diverse areas.

*Recommended as a breadth subject for Arts and Music students. Note that this subject does not form a pathway to any further mathematics and statistics subjects.*

### UNIB10006 Critical Thinking With Data

This subject teaches students to become critical users of data-based evidence. Future journalists, political scientists, sociologists, lawyers, health professionals, psychologists, environmental scientists, business people, engineers, scientists and teachers will develop skills in identifying the strengths and weaknesses of arguments and reports based on quantitative evidence, and learn to evaluate reasoning that uses probabilistic ideas.

*This is a University breadth subject and is available as breadth to students of most undergraduate degree programmes including the Bachelor of Science.*

This information is for students who completed UMEP Extension Mathematics during secondary school.

- Students who have completed MAST10018 Linear Algebra Extension Studies may be granted credit in their Bachelor degree program for MAST10007 Linear Algebra.
- Students who have completed MAST10019 Calculus Extension Studies may be granted credit in their Bachelor degree program for MAST10006 Calculus 2 (additional reading on sequences and series may be required before commencing studies in certain subjects).

Being granted credit provides the option of having a lighter study load at some stage during the degree. Alternatively, students may decide not to receive credit. In this case, if needed, MAST10018 and MAST10019 may just be used as a prerequisite for other subjects in their degree.

Students who have completed both semesters of the UMEP program (MAST10018 and MAST10019) will be able to take one of the following subjects in their first semester of first year, according to their grades in MAST10018 and MAST10019:

Subject | Prerequisite | Comments |
---|---|---|

MAST20004 Probability | Grade of at least 60 in MAST10019 and a pass in MAST10018 | Required for a major in Actuarial Studies |

MAST20006 Probability for Statistics | Pass in both MAST10018 and MAST10019 | Useful for students considering a specialisation in statistics |

MAST20009 Vector Calculus | Pass in both MAST10018 and MAST10019 | Required and/or recommended for majors in Mathematics or Physics |

In general, we recommend that students take MAST20026 Real Analysis in their second semester of first year. Note that Real Analysis is a prerequisite for most level-3 mathematics and statistics subjects.

### Engineering systems major

Depending on the type of engineering major, we recommend the following subjects.

| Semester 1 | Semester 2 |
---|---|---|

Electrical systems | MAST20009 Vector Calculus | MAST20026 Real Analysis |

Other engineering | MAST20009 Vector Calculus | MAST20030 Differential Equations |

Completion of MAST20009 Vector Calculus and MAST20030 Differential Equations satisfies the requirement for MAST20029 Engineering Mathematics.

### Bachelor of Biomedicine

Students taking the Bioengineering Systems major who have completed both semesters of the UMEP program (MAST10018 and MAST10019) will receive credit for the first year mathematics component of the Bioengineering Systems major in the Bachelor of Biomedicine.

Students taking other majors of the Bachelor of Biomedicine who have completed MAST10018 and MAST10019 can gain exemptions from MAST10011 Experimental Design and Data Analysis and MAST10016 Mathematics for Biomedicine and receive 25 points of Level 1 Selective credit.

**NOTE: Students are strongly encouraged to seek course advice from their Faculty and the School of Mathematics and Statistics before selecting subjects in their first year of university study.**

For information about the UMEP mathematics courses (content, assessment, etc.) please contact Anthony Mays (anthony.mays@unimelb.edu.au) or John Banks (john.banks@unimelb.edu.au).

For questions about enrolment, please contact extension-program@unimelb.edu.au