Teaching

2018-now, The University of Melbourne.

2024 Semester 1: 

Torus parametrisation: https://www.gsn-lib.org/docs/nodes/MeshTorusNode.php

Watch the Video (parametrization of torus): https://www.youtube.com/watch?v=heFhbV5J_bY&ab_channel=DanGries

Möbius band: https://www.youtube.com/watch?v=pgbHR290RW8&t=9s&ab_channel=romullus3d

Plot vector fields in R^2: https://www.geogebra.org/m/QPE4PaDZ

Plot vector fields in R^3: https://www.geogebra.org/m/u3xregNW

Local extrema: https://byjus.com/maths/saddle-points/


Divergence of a vector field: https://www.youtube.com/watch?v=c0MR-vWiUPU&ab_channel=KhanAcademy

Curl of a vector field: https://www.youtube.com/watch?v=eEwZeY51mT0&ab_channel=KhanAcademy

     Laplacian intuition: https://www.youtube.com/watch?v=EW08rD-GFh0&ab_channel=KhanAcademy


      Cylindrical coordinates: https://mathinsight.org/applet/cylindrical_coordinates

 Spherical coordinates: https://mathinsight.org/applet/spherical_coordinates

Space curve: https://www.math3d.org/motion

Line integral of a scalar function: https://www.geogebra.org/m/ma2n5KNH

Line integral of a vector field: https://www.geogebra.org/m/fnCKwmTP

Double integral: https://www.geogebra.org/m/deu55wzs

Triple integral visualizer: https://www.geogebra.org/m/eqbrwepa

Triple integral cylindrical: https://www.geogebra.org/m/xxdcmahc

Triple integral spherical: https://www.geogebra.org/m/fcufcs74

      Maxwell-https://en.wikipedia.org/wiki/James_Clerk_Maxwell

Video: Episode 39: Maxwell's Equations - The Mechanical Universe: https://www.youtube.com/watch?v=SS4tcajTsW8&t=927s&ab_channel=caltech

Electromagnetic Wave and Maxwell's Equations.


https://www.geogebra.org/calculator

      CalcPlot3D: https://c3d.libretexts.org/CalcPlot3D/index.html

      3d surface plotter: https://academo.org/demos/3d-surface-plotter/


2023 Semester 2: 

Subject Coordinator: Dr Christine Mangelsdorf, mangel@unimelb.edu.au

Lecture

Monday, Wednesday, Friday, 10am-11:00am in the JH Michell theatre, Peter Hall building

Tutorial:

Monday 1:00pm-2:00pm, Peter Hall-G14

Consultation hours:

Monday (by 16 Oct 2023) 2:00-5:00pm.


25 Oct 2023: 2-5pm. 


Subject Coordinator: Craig Hodgson, craigdh@unimelb.edu.au

Lecture

Monday, Wednesday, Friday, 11am-12:00pm in the JH Michell theatre, Peter Hall building

Tutorial:

Wednesday 1:00pm-2:00pm, Peter Hall-G50

Consultation hours:

Monday 2:00-5:00pm.


Some links to show in class (They are available to students in the LMS modules.): 


Illustrating how solutions depend of the initial conditions: 

https://melbapplets.ms.unimelb.edu.au/2021/07/07/exploring-an-ode/

Real world population data:

https://ourworldindata.org/grapher/population?time=-1000..2013

In recent times, populations in some places noticeably flatten, e.g. Europe. As predicted by the logistic model.

Applets to help visualise the logistic model and logistic with harvesting:

Logistic model: https://www.geogebra.org/m/BTo0Ux6s
Logistic with harvesting: https://www.geogebra.org/m/ZeEbVDfN
 These applets show the phase plot (rotated by 90o) on the left-hand side and a solution on the right.

Here is an applet simulating a spring with external force

https://www.geogebra.org/m/y4Ercw2b


Tacoma Narrows Bridge collapse and show the famous video of this. See 

https://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_(1940) https://en.wikipedia.org/wiki/File:Tacoma_Narrows_Bridge_destruction.ogv

CalcPlot3D: https://c3d.libretexts.org/CalcPlot3D/index.html


3d surface plotter: https://academo.org/demos/3d-surface-plotter/

 

Not differentiable surfaces: 

https://math.stackexchange.com/questions/620627/showing-that-the-function-given-by-fx-y-fracxy-sqrtx2y2-and-f0-0

https://en.wikipedia.org/wiki/Conical_surface


Gradient descent is an important method in statistics, data science & machine learning for finding (approximate) local minima of a multivariable function.

https://echo360.net.au/media/22509125-149f-4b4b-a219-c9adc4ea84cc/public

 

 

2022 Semester 2: 

Linear Algebra (MAST10007_2022_SM2) https://handbook.unimelb.edu.au/2022/subjects/mast10007

2018 Semester 2: 

Advanced Topics in Geometry and Topology (MAST90124)

https://handbook.unimelb.edu.au/2018/subjects/mast90124

Course webpage: https://sites.google.com/site/yapingyanghomepage/teaching/2018-semester-2

2015-2017: University of Massachusetts Amherst.

Spring 2017

1. Math412:Introduction to Abstract algebra II, room: LGRT 173,

Tu Th 8:30am-9:45AM,

Course webpage: https://sites.google.com/site/yapingyanghomepage/teaching/spring2017-math412

2. Math 235: Introduction to Linear Algebra, Tu Th 10:00am-11:15AM, Room: LGRT 121

Course webpage: https://sites.google.com/site/yapingyanghomepage/teaching/spring2017_math235

Course ID: yang81334 (you will receive a 50% penalty on late assignments).

Fall 2016:

1. Math 411-02 Introduction to abstract algebra I https://sites.google.com/site/yapingyanghomepage/teaching/fall2016_math411

2. Math 132.07, Calculus 2

Spring 2016:

1. Math 132.07, Calculus 2

2. Math 412, Introduction to Abstract algebra II

Fall 2015:

1. Instructor, Math 132H.01, honors Calculus 2, University of Massachusetts Amherst.

2. Instructor, Math 132H.02, honors Calculus 2, University of Massachusetts Amherst.

The course webpage https://sites.google.com/site/yapingyanghomepage/teaching/fall-2015_math132h

Spring 2015:

1. Instructor, Math 132.12 Calculus 2, University of Massachusetts Amherst.

2. Instructor, Math 132.13 Calculus 2, University of Massachusetts Amherst.

2009-2014: Teaching Assistant, Northeastern University, Boston, U.S.A

Spring 2014: Teaching Assistant, Math 2331 Linear Algebra.

Fall 2013: Instructor, Math 1215 Mathematical thinking.

Spring 2013: Instructor, Math 1231 Calculus for Business and Economics.

Fall 2012: Instructor, Math 1215 Mathematical thinking.

Spring 2012:Teaching Assistant, Math 2280 and 2285 Statistics and Software.

Fall 2011: Recitation Leader, Math 1241 Calculus 1.

Spring 2011: Instructor, Math 2321 Calculus 3 for Science and Engineering.

Fall 2010: Recitation Leader, Math 2321 Calculus 3 for Science and Engineering.

Spring 2010: Instructor, Math 2280 Statistical thinking.

Fall 2009: Recitation Leader, Math 2321 Calculus 3 for Science and Engineering.