Courses

Explore the power of Taylor polynomials for approximations and analysis in this 22-minute video. Dive into the concept of approximating cos(x), then generalize the approach to other functions. Examine the Taylor series for e^x and uncover the geometric meaning of its second term. Conclude by addressing convergence issues, gaining a comprehensive understanding of this fundamental mathematical tool. Suitable for those interested in advanced calculus and mathematical analysis.

Learn to solve numerical problems involving Taylor series and Taylor's theorem in the context of complex analysis through this 16-minute mathematics tutorial. Master the application of Taylor series expansion for complex functions and develop skills in complex variable integration techniques. Work through practical examples that demonstrate how to apply Taylor's theorem to complex integration problems, covering essential concepts needed for engineering mathematics courses. Gain proficiency in manipulating complex variables and understanding their integration properties, with content suitable for BSc, BTech, and various competitive examination preparations including UPSC, CTET, NET, and JEE.

Explore the intricacies of Taylor and Maclaurin Series in this comprehensive 30-minute video lecture. Delve into advanced calculus concepts, starting with the Taylor Series for a polynomial centered at 1 and progressing to the Taylor Series of ln(x) at x = 2 and e^2x at a = 3. Tackle challenging problems, including integrating x*cos(x^3) and (e^x-1)/x as power series. Master the art of integrating power series and learn to apply these techniques to evaluate limits. Enhance your understanding of series expansions and their applications in calculus through practical examples and problem-solving exercises.

Learn about secimport, an innovative eBPF-based sandbox toolkit for Python applications, in this 20-minute PyCon Israel conference talk. Discover how to implement granular security controls by enforcing specific syscalls at the module level, effectively reducing potential attack surfaces while maintaining optimal performance. Explore the toolkit's capabilities for tracing and profiling Python applications, and understand how to establish and enforce robust security policies that protect your code without compromising functionality.

Kick off your data analysis journey by diving into SQL, guided by the music of Taylor Swift's discography. This course is designed to help you ask the right questions to a database, find specific information, and comprehend basic data relationships. Perfect for beginners, all you need is a love for music and the curiosity for data.

Dive into the world of SQL Joins guided by the unforgettable hits of Taylor Swift. This course is designed to expand your data analysis skills by exploring the concept of table joins. With Taylor's discography as a backdrop, learn how to uncover intricate relationships within a database. This course blends the love for music with the thrill of data discovery.

This learning path is a fun, accessible introduction to SQL, one of the most popular database query languages. It uses Taylor Swift's discography as your database. Your data “Love Story” starts here!

Join Pluralsight President & COO Somit Goyal for an insightful—and even amusing!—fireside chat with Johnny C. Taylor, Jr., SHRM-SCP, President & CEO at the Society for Human Resource Management (SHRM).

Explore the customization capabilities of OpenSSF Scorecard's new feature, Scorecard Structured Results, in this 35-minute conference talk by Adam Korczynski and David Korczynski from Ada Logics. Learn how to tailor supply-chain security policies using more than 50 different software supply chain security heuristics. Discover the internal workings of Scorecard Structured Results, its potential use cases, and practical examples of implementing custom policies with popular policy engines. Gain insights into automating software supply chain security assessments and adapting them to diverse software ecosystems. Understand how this feature allows users to decide which specific vulnerability analysis tools should be used by dependencies to analyze source code, enhancing the overall security of software projects.

Explore an innovative approach to finding Taylor series using differential equations in this engaging 24-minute video. Learn how to apply mathematical concepts to solve complex problems as Michael Penn guides you through the process. Discover the intersection of Taylor series and differential equations, gaining valuable insights into advanced mathematical techniques. Enhance your problem-solving skills and deepen your understanding of calculus and series expansions.

Follow photographer Brian Taylor as he combines Photoshop and other modern imaging tools with photographic processes that were invented in the 1800s.

This 50-minute conference talk at BSidesCharm 2025 prepares security professionals for investigating and responding to generative AI chatbot incidents. Learn practical methods for handling security breaches when LLM-powered virtual agents start behaving inappropriately or leaking sensitive customer information. Discover specialized techniques for isolating attacks, gathering evidence, and determining root causes using AI defense tooling and LLM guardrails. Gain a comprehensive incident response playbook specifically designed for GenAI systems and understand the critical preparation steps needed before your organization faces a chatbot security crisis. Presented by Allyn Stott, senior staff engineer at Airbnb with extensive experience in threat detection and incident response, who has spoken at numerous security conferences including Black Hat and holds a Master's in High Tech Crime Investigation from The George Washington University.

Explore Taylor polynomial approximations and their accuracy bounds before diving into the construction of Riemann integrals in this advanced mathematics lecture from MIT's Real Analysis course. Begin by learning how to estimate the closeness of Taylor expansions to their original functions through bounding the remainder term, a crucial skill for understanding approximation theory. Transition into the foundational construction of Riemann integrals, discovering how these mathematical tools were originally developed to calculate areas of complex geometric figures and understanding their central role across all branches of mathematics. Master the theoretical underpinnings of integration theory while building essential analytical skills for advanced mathematical study.

Explore the advanced mathematical concept of Ruelle Taylor resonances in the context of higher rank Anosov actions in this hour-long lecture presented by T. Weich from the University of Paderborn. Delve into analytic techniques applied to dynamics and geometry, gaining insights into this complex topic within the field of mathematical physics. Enhance your understanding of dynamical systems and their geometric properties through this in-depth presentation.

Explore the concept of approximating functions using Taylor polynomials in this comprehensive lecture. Delve into the mathematical principles behind Taylor series expansions and learn how to construct polynomial approximations for complex functions. Gain a deep understanding of the accuracy and limitations of Taylor polynomials, and discover their practical applications in various fields of mathematics and engineering. Through clear explanations and worked examples, master the techniques for determining the appropriate degree of polynomial approximation and assessing the error bounds. Enhance your calculus skills and broaden your mathematical toolkit with this in-depth exploration of function approximation methods.

Elevate your SQL skills to the next level with the power of SQL functions while exploring Taylor Swift's discography. This course is perfectly crafted for learners who have grasped the basics of SQL and are ready to discover how functions can enhance data analysis and reporting. Dive into the world of counting, summarizing, and unique identifying features of data with a musical twist.

Explore an advanced mathematics lecture on almost-prime times in horospherical flows, delivered by Taylor McAdam at the Hausdorff Center for Mathematics. Delve into effective dynamical results for horospherical flows on the space of lattices using the "thickening" method of Margulis. Discover how these findings are applied to study the distribution of almost-prime times in horospherical orbits and their connection to Sarnak's Mobius disjointness conjecture. Examine topics such as the space of lattices, subgroup actions, rigidity of horospherical actions, equidistribution of primes, and the horocycle flow at prime times. Gain insights into qualitative and effective equidistribution of continuous flows and arithmetic progressions in this 42-minute presentation, part of the Hausdorff Trimester Program "Dynamics: Topology and Numbers" conference.

Explore Rayleigh-Taylor mixing in porous media through a 24-minute conference talk delivered by Guido Boffetta from the University of Turin. Recorded as part of the Interfaces and Mixing in Fluids, Plasmas, and Materials conference at the Kavli Institute for Theoretical Physics, this presentation delves into the complex interactions between fluids and porous materials. Gain insights into how Rayleigh-Taylor instabilities behave in these unique environments, and understand the implications for various fields including geophysics, materials science, and fluid dynamics. Connect the principles of quantum metrology to fundamental physics applications, ranging from dark matter searches to gravitational wave detection. Benefit from the cross-disciplinary approach of the conference, which brings together experts from optics, condensed matter, atomic physics, quantum information, particle physics, and gravitational physics to foster new scientific discoveries and collaborations.

If you're looking to analyze large amounts of text and gain deeper insight into music, try this case study. You will put your natural language processing and machine learning skills to use answering interesting questions about Taylor Swift's lyrics. We will provide you with the context, data, and instructions that you need to analyze themes and sentiments in Taylor Swift's albums. You'll explore how she thinks about time, especially Midnight, as well as day and night. You'll create visualizations and see her music in a whole new way.

Learn how to apply Taylor's Inequality to approximate error when using Taylor polynomials for function representation in this 47-minute mathematics video lecture. Master techniques for finding upper bounds on error through multiple worked examples and discover methods to determine the necessary number of terms needed in approximations to guarantee error falls below specified thresholds. Build upon foundational knowledge of Taylor polynomials and series while exploring practical applications of error approximation in calculus.