MANUELA GIROTTI

Here you can find my Teaching Statement and my Teaching Dossier (last update: February 2024).

Some food for thought:
When Will I Ever Use Math?
Why do we have to learn proofs!?

Emory teaching

MATH 789 Topics in Analysis - Approximation Theory (Fall 2024): syllabus.

MATH 318 Complex Variables (Fall 2024): syllabus.

MATH 250 Foundamentals of Mathematics (Spring 2024): syllabus.

• Proofs (direct, contrapositive, by contradiction): exercises.
• Sets: exercises.
• Partitions and pigeonhole principle: exercises.
• Partitions of integers: notes.
• Induction Principle: exercises and more exercises.
• Equivalence Relations: notes/exercises.
• Diophantine equations: notes.

Past teaching

SMU

MATH 2303 Differential Equations I (Winter 2023): syllabus.

• Van Meegeren's art forgeries: beamer presentation.
• Compartmental analysis: exercises.
• Spring systems and electrical circuits: exercises and Jupyter notebook (beat phenomenon).

MATH 3441 Real Analysis I (Fall 2022): syllabus.

MATH 3406 Differential Equations II (Winter 2022): syllabus.

• ODEs with Python: Jupyter notebook.
• The Van der Pol oscillator: notes and link to the Jupyter notebook.
• The predator-prey model (Lotka-Volterra): Jupyter notebook.
• Modelling infectious diseases (SIR model and COVID pandemic): Jupyter notebook.

MATH 4442 Real Analysis II (Winter 2022): syllabus.

MATH 3441 Real Analysis I (Fall 2021): syllabus.

• Why do we care about metric spaces? (scribbles): Fréchet.
• Pointwise vs Uniform Convergence (scribbles): pointwise VS uniform.
• Closed unit ball in normed vector spaces: unit ball.
• The Cantor set and the Devil's staircase: Cantor set.

JAC

MATH NYB Calculus II (Fall and Winter 2019): syllabus.

MATH 015 Algebra and Trigonometry (Fall and Winter 2019): syllabus.

CSU

MATH 530 Mathematics for Scientists and Engineers (Fall 2018): syllabus.

MATH 345 Differential Equations (Spring 2018 - Honors course): syllabus.

• Using MATLAB to study ODEs: notes1 and notes2.
• Conservative systems with one degree of freedom: potential.
• A model for competitive markets: Arrow-Block-Hurwicz theorem.

MATH 317 Advanced Calculus of One Variable (Fall 2017): syllabus for my section (MATH 317-01).

• Construction of Q: rational numbers.
• Notes on R: real numbers and Cantor.
• The Riemann integral: Riemann integral.
• Notes on series: series and power series.
• Introductory notes on Fourier series: Fourier.

MATH 369 Linear Algebra (Spring 2017): syllabus for my section (MATH 369-05).

• Quadratic forms: conics.

CU

Instructor: MATH 205 Section C (Winter 2011) and Section A (Fall 2011).

Tutor: MATH 201 (Winter 2014).

Technical Assistant: WEBWorK system for the courses MATH 200-201-202-203-204-205 (Fall 2012 till Summer 2014).

Projects

I've been developing some little didactic projects over the years: Github repositories.
The programming languages I'm familiar with are: HTML, C++, Java, Python. I also have many years of experience with using Matlab and Maple.