Unit outline_

# MATH1050: Mathematics Toolbox for Science

## Overview

Mathematics is a powerful tool in Science. It is used to interpret observations, to formulate predictions, create models, refine theory and communicate scientific reasoning in many disciplines. In this unit you will learn how Mathematical ideas are applied across Science. You will see that Mathematics plays a fundamental role in the Life and Environmental Sciences, in Medicine and in Health, as well as in physical sciences. You will meet familiar ideas such as calculus and exponentials now put to work to solve practical scientific problems, and you will be introduced to powerful new concepts such as matrices and differential equations. You will use public domain technology to perform calculations, do algebra and draw graphs which will enable you to work on interesting real-world scenarios. At the end of this unit you will be equipped to use mathematical ideas confidently in the disciplinary and interdisciplinary contexts that you will meet in your degree and beyond. This unit is designed to complement DATA1001 in the Science core. Students intending to major in Physics or Chemistry are recommended to take MATH1021 and MATH1002. Students majoring in Mathematics, Statistics or Financial Mathematics and Statistics must take MATH1021 and MATH1002.

### Unit details and rules

Academic unit Mathematics and Statistics Academic Operations 6 None None MATH1002 or MATH1021 or MATH1023 or MATH1921 or MATH1902 or MATH1923 or MATH1933 or MATH1931 or (MATH1011 and MATH1014) or (MATH1013 and MATH1014) or (MATH1011 and MATH1013) or MATH1001 or MATH1003 or MATH1901 or MATH1906 or MATH1903 or MATH1907 NSW HSC Mathematics Advanced Yes

### Teaching staff

Coordinator Mary Myerscough, mary.myerscough@sydney.edu.au Mary Myerscough

## Assessment

Type Description Weight Due Length
Supervised exam

Final Exam
Multiple choice and written calculations
50% Formal exam period 2 hours
Outcomes assessed:
Assignment Assignment 1
Written calculations in total 2-4 pages.
5% Week 04
Due date: 16 Mar 2023 at 23:59

Closing date: 26 Mar 2023
n/a
Outcomes assessed:
Multiple choice quiz
15% Week 07
Due date: 06 Apr 2023 at 23:59

Closing date: 06 Apr 2023
40 minutes
Outcomes assessed:
Assignment Assignment 2
Longer written project in total 5-10 pages
20% Week 11
Due date: 11 May 2023 at 23:59

Closing date: 21 May 2023
n/a
Outcomes assessed:
Small test Weekly Quizzes
Multiple choice questions
8% Weekly Week 2-6, 8-12
Outcomes assessed:
Participation Workshops
Participation in workshops
2% Weekly 2 hours/week
Outcomes assessed:

### Assessment summary

• Assignments:  There are two assignments. Each must be submitted electronically, as one single typeset or scanned PDF file only, via Canvas by the deadline. Note that your assignment will not be marked if it is illegible or if it is submitted sideways or upside down. It is your responsibility to check that your assignment has been submitted correctly and that it is complete (check that you can view each page). Late submissions will receive a penalty. A mark of zero will be awarded for all submissions more than 10 days past the original due date. Further extensions past this time will not be permitted.
• Quiz: One quiz will be held online through Canvas. The quiz is 40 minutes and has to be submitted by the closing time of 23:59 on the due date. The quiz can be taken any time during the 24 hour period before the closing time. The better mark principle will be used for the quiz so do not submit an application for Special Consideration or Special Arrangements if you miss a quiz. The better mark principle means that the quiz counts if and only if it is better than or equal to your exam mark. If your quiz mark is less than your exam mark, the exam mark will be used for that portion of your assessment instead.
• Online Quizzes: There are ten weekly online quizzes (equally weighted) and the marks for the best eight count. Each online quiz consists of a set of randomized questions. You should not apply for special consideration for the quizzes. The better mark principle will apply for the total 8% - i.e. if your overall exam mark is higher, then your 8% for the Webwork quizzes will come from your exam. The deadline for completion of each quiz is 23:59 on Friday (starting in week 2). The precise schedule for the quizzes is found on Canvas. We recommend that you follow the due dates outlined above to gain the most benefit from these quizzes.
• Workshop Participation: This is a satisfactory/non-satisfactory mark assessing whether or not you participate in class activities during the workshops. It is 0.25 marks per tutorial class up to 8 tutorials (there are 12 workshops).
• Final Examination: The final exam for this unit is compulsory and must be attempted. Failure to attempt the final exam will result in an AF grade for the course. Further information about the exam will be made available at a later date on Canvas. If a second replacement exam is required, this exam may be delivered via an alternative assessment method, such as a viva voce (oral exam). The alternative assessment will meet the same learning outcomes as the original exam. The format of the alternative assessment will be determined by the unit coordinator.

### Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

Result name

Mark range

Description

High distinction

85 - 100

Representing complete or close to complete mastery of the material.

Distinction

75 - 84

Representing excellence, but substantially less than complete mastery.

Credit

65 - 74

Representing a creditable performance that goes beyond routine knowledge and understanding, but less than excellence.

Pass

50 - 64

Representing at least routine knowledge and understanding over a spectrum of topics and important ideas and concepts in the course.

Fail

0 - 49

When you don’t meet the learning outcomes of the unit to a satisfactory standard.

### Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

• Deduction of 5% of the maximum mark for each calendar day after the due date.
• After ten calendar days late, a mark of zero will be awarded.

The Current Student website  provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

## Learning support

### Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

### Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

### Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

## Weekly schedule

WK Topic Learning activity Learning outcomes
Week 01 Mathematical basics (Algebra with software, changing subjects of formulae, orders of magnitude, numbers, etc). Periodic functions. Curve fitting. Applications. Lecture and tutorial (5 hr)
Week 02 Exponentials, exponential growth and decay, changing from one base to another, doubling time. Applications. Lecture and tutorial (5 hr)
Week 03 Logarithms to base 10, 2, and e. Logarithmic processes, log-log and log-lin plots, pH and pKa. Lecture and tutorial (5 hr)
Week 04 Complex numbers. Functions and mappings. Recurrence relations. Applications. Lecture and tutorial (5 hr)
Week 05 Matrices: basic arithmetic, linear equations, population models and graph theory Lecture and tutorial (5 hr)
Week 06 Eigenvectors and eigenvalues, Leslie matrix models of populations. Lecture and tutorial (5 hr)
Week 07 Continuous change: the derivative as a measure of change. Approximations to the derivative. Higher order derivatives: rates of change of rate of change. Applications. Lecture and tutorial (5 hr)
Week 08 Continuous accumulation: the integral as a measure of accumulation, calculating averages and weighted averages, rates of accumulation, links between differentiation and integration, functions defined as integrals. Applications. Lecture and tutorial (5 hr)
Week 09 Functions of two variables, graphing functions of two variables: surface and contour plots. Partial derivatives. Lecture and tutorial (5 hr)
Week 10 Differential equations, exponential growth, logistic growth, interpretation of DEs without a solution. Lecture and tutorial (5 hr)
Week 11 Systems of differential equations, epidemiological models, spread of infectious diseases Lecture and tutorial (5 hr)
Week 12 Approximation: Approximating a curve with a line, or another curve. Building models. Lecture and tutorial (5 hr)

### Attendance and class requirements

• Lecture attendance: You are expected to attend lectures. If you do not attend lectures you should at least follow the lecture recordings available through Canvas.
• Workshop attendance: Workshops (one per week) start in Week 1. You should attend the workshop given on your personal timetable. Attendance at workshops and participation will be recorded to determine the participation mark. Your attendance will not be recorded unless you attend the workshop in which you are enrolled. We strongly recommend you attend workshops regularly to keep up with the material and to engage with the tutorial questions.

### Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

## Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

At the completion of this unit, you should be able to:

• LO1. Perform appropriate mathematical operations both with pen-and-paper and using suitable software
• LO2. Apply mathematical ideas to analysing problems in science and medicine
• LO3. Determine where a mathematical approach is required in scientific problem solving and what that approach should be
• LO4. Communicate mathematical ideas clearly and correctly in written and spoken form

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

 GQ1 Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline. GQ2 Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem. GQ3 Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context. GQ4 Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies. GQ5 Inventiveness Generating novel ideas and solutions. GQ6 Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues. GQ7 Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries. GQ8 Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context. GQ9 Influence Engaging others in a process, idea or vision.

### Outcome map

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

## Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

This is the first time this unit has been offered.