Numerical Methods and Optimization in Python

🎓 Unlock the Secrets of Numerical Methods and Optimization in Python with Expert Holczer Balazs{.course-instructor}!

🚀 Course Title: Numerical Methods and Optimization in Python

🧮 Headline: Master Gaussian Elimination, Eigenvalues, Numerical Integration, Interpolation, Differential Equations, and Operations Research through practical Python implementations!

Overview: This comprehensive course is your gateway into the world of numerical methods and optimization algorithms within the versatile Python programming language. We'll delve into concrete implementations and the underlying numerical principles that power these computational techniques. 🔍

Course Structure:

Section 1 - Numerical Methods Basics

• Understand the fundamentals of numerical methods.
• Learn about floating point representation and common errors.
• Explore the performance differences between C, Java, and Python in numerical computations.

Section 2 - Linear Algebra and Gaussian Elimination

• Grasp the basics of linear algebra.
• Master matrix multiplication and Gauss-elimination techniques.
• Discover how to apply these methods to real-world problems like portfolio optimization.

Section 3 - Eigenvectors and Eigenvalues

• Dive into the concepts of eigenvectors and eigenvalues.
• Explore their applications in machine learning, particularly Principal Component Analysis (PCA).
• Uncover the secret behind Google's PageRank algorithm.

Section 4 - Interpolation

• Learn the theory behind Lagrange interpolation.
• Get hands-on with implementation and practical applications of interpolation methods.

Section 5 - Root Finding Algorithms

• Solve non-linear equations using various root finding techniques.
• Understand and apply Newton's method and the bisection method.

Section 6 - Numerical Integration

• Get to grips with the rectangle, trapezoidal, and Simpson's methods of numerical integration.
• Discover the Monte-Carlo approach for integral approximation.

Section 7 - Differential Equations

• Learn solving strategies for differential equations.
• Practice Euler's method and the more sophisticated Runge-Kutta method.
• Apply these methods to classic problems like the pendulum and ballistics.

Section 8 - Numerical Optimization (in Machine Learning)

• Unravel the gradient descent algorithm and its variants: Stochastic Gradient Descent, ADAGrad, RMSProp, and ADAM optimizer.
• Understand the theory behind these algorithms and see their implementation in machine learning contexts.

🛠️ For Beginners: No need to worry if you're new to Python programming! The course concludes with chapters dedicated to teaching the fundamentals and basics of Python, ensuring everyone can follow along and enhance their coding skills. 🧙‍♂️

Join us on this mathematical adventure where theory meets practice, and Python turns complex algorithms into manageable code. Whether you're a data scientist, a machine learning enthusiast, or simply fascinated by the power of numerical methods, this course will equip you with the knowledge and skills to solve real-world problems effectively.

👩‍🏫 Instructor Note: I'm excited to guide you through these concepts and techniques. Whether you're a Python veteran or just starting out, there's something new for everyone. Let's embark on this journey together and unlock the full potential of numerical methods and optimization!

Thanks for choosing this course, and I can't wait to see you in the next lesson! 🌟