Welcome to the SIO Math Workshop!

The Math Workshop is a student-hosted program designed to welcome and support incoming students as they begin their academic journey. This workshop is offered as a refresher and introduction to mathematical concepts and problems you will encounter in your first year courses.

Over the course of the workshop, participants will: * Work through interactive examples, including Jupyter notebooks with guided exercises. * Build connections with peers and student mentors who have recently taken these same courses.

The workshop is open to all incoming students, regardless of prior preparation. Our goal is to create a welcoming, collaborative environment where students can build confidence and curiosity in mathematics before classes begin.

By the end of the program, participants will have: * A clearer sense of what to expect in first-year math courses. * A set of study resources and practice materials they can revisit. * A stronger connection to the campus math community.

Workshop Materials

• Schedule
  • Day 1 - 09/22
  • Day 2 - 09/23
• Day 1
  • Algebra
    • 1 | FIRST SECTION
      • 1.1 FIRST SUBSECTION
  • Geometry Trig
  • Complex Numbers
    • Overview
    • 1 | What are complex numbers?
      • 1.1 The need for complex numbers
      • 2 | Definitions
    • 2 | Visualizing complex numbers
      • 2.1 The complex plane
      • 2.2 Polar coordinates
      • 2.3 Euler’s formula
    • 3 | Operating on complex numbers
      • 3.1 Addition and Subtraction
      • 3.2 Multiplication
      • 3.3 Division
      • 3.4 Powers
      • 3.5 Roots
    • 4 | References
    • 5 | Appendix
      • 5.1 Comparing complex numbers
      • 5.2 A brief history of complex numbers
  • Limits and Derivatives
    • Learning Objectives
    • 1 | Limits
      • 1.1 Kinds of Limits
    • 2 | Derivatives
      • 2.1 Derivative Rules Cheat Sheet
      • 2.2 Useful Derivatives
      • 2.3 Derivative Notation
    • Practice Problems
      • 1. What is the instantaneous rate of change at \(x=2\) of \(f(x)=\frac{x^2-2}{x-1}\)
        • solution:
        • solution:
        • solution:
  • Integrals
    • 1 | Integration
      • 1.1 Traveling in a Car
      • 1.2 Riemann Sum
      • 1.3 Car example (with Δt = 1)
    • 2 | Introducing the Integral
      • 2.1 Applying to our car example
      • 2.2 Computing the Integral
        • 2.2.1 Step 1: Expand the function
        • 2.2.2 Step 2: Apply the Power Rule for Integration
        • 2.2.3 Step 3: Evaluate at the Bounds (Fundamental Theorem of Calculus)
      • 2.3 The Fundamental Theorem of Calculus
      • 3.1 Power Rule
      • 3.2 Exponential Functions
      • 3.3 Logarithmic Function
      • 3.4 Sine and Cosine
      • 3.5 Other Trigonometric Functions
      • 3.6 Linear Combination Rule
      • 3.7 Integration by Substitution (u-substitution)
      • 3.8 Inverse Trigonometric Functions
      • 3.9 Hyperbolic Functions
      • 3.10 Special Rules / Tricks
      • 3.11 Integration by Parts
      • 3.11.1 Example
    • Practice Problems
  • Vector Calculus
    • 1 | FIRST SECTION
      • 1.1 FIRST SUBSECTION
  • Taylor Expansions and Series Solutions
    • 1 | Introduction
    • 2 | Taylor Expansions
      • 2.2 Building Intuition on Taylor Series
      • 2.3 Exercises
      • 2.4 List of common Taylor expansions:
    • 3 | Power Series
    • 4 | Fourier Series
  • Fourier Analysis
    • 1 | FIRST SECTION
      • 1.1 FIRST SUBSECTION
  • Ordinary Differential Equations
    • 1 | Notation
    • 2 | Classification of ODEs
      • 2.1 What is an ODE?
      • 2.2 Order of an ODE
      • 2.3 Linear vs Non-linear ODEs
      • 2.4 Homogeneous vs Inhomogeneous ODEs
    • 3 | An Introduction to Solving ODEs
      • 3.1 Boundary and Initial Conditions
      • 3.2 First Order ODEs
        • 3.2.1 Separable First Order ODEs
        • 3.2.2 Integrating Factor
      • 3.3 Second Order ODEs
        • 3.3.1 Classification (again)
        • 3.3.2 Solution by Ansatz
• Day 2
  • Intro to Statistics
    • 1 | FIRST SECTION
      • 1.1 FIRST SUBSECTION
  • Distribution Functions
    • 1 | FIRST SECTION
      • 1.1 FIRST SUBSECTION
  • Data Workshop 1
    • 1 | FIRST SECTION
      • 1.1 FIRST SUBSECTION
  • Linear Algebra 1
    • 1 | Why Linear Algebra?
      • 1.1 Application of Linear Algebra
    • 2 | Review - Scalars, Vectors, Matrices, Tensors and Dimensions (Oh my!)
      • 2.1 Notation
      • 2.2 Scalars
      • 2.3 Vectors
      • 2.4 Linear Combinations and Spans
      • 2.5 Matrices
      • 2.6 Tensors
    • 3 | The Algebra in Linear Algebra
      • 3.1 | Matrix Addition
      • 3.2 | Matrix Multiplication
      • 3.3 | Linear Transformations
    • 4 | The Determinant and Inverse Matrices
  • Linear Algebra 2
    • 1 | Introduction and motivation
    • 2 | Definitions & finding eigenvectors
    • 3 | Diagonalization
      • 3.1 Performing a diagonalization
    • 4 | Why?
  • Statistics in Practice
    • 1 | FIRST SECTION
      • 1.1 FIRST SUBSECTION
  • Data Workshop 2
  • MATLAB
  • Raw Data
    • Reading in the data
    • Removing NaNs
    • Interpolation
    • Filtering Data
    • Spectral Analysis - Fourier Space
  • Python
  • Raw Data
    • Reading in the data
    • Removing NaNs
    • Interpolation