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Fundamentals Tools of Probability and Combinatorics

person icon AKHIL VYDYULA

4.4

Fundamentals Tools of Probability and Combinatorics

Make informed decisions with probability and combinatorics

updated on icon Updated on Feb, 2025

language icon Language - English

person icon AKHIL VYDYULA

category icon Finance and Accounting,Finance,ChatGPT

Lectures -20

Duration -2 hours

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Course Description

Are you fascinated by the world of uncertainty and counting? Do you want to gain a fundamental understanding of probability and combinatorics? If so, our "Introduction to Probability and Combinatorics" course is the perfect starting point for your journey into this captivating field of mathematics.

Course Overview:

Probability and combinatorics are two fundamental branches of mathematics that underpin a wide range of disciplines, from statistics and data science to engineering and computer science. In this course, you will explore the core concepts of both probability and combinatorics, building a strong foundation for advanced studies and real-world applications.

Who Should Enroll:

  • Students and professionals seeking a foundational understanding of probability and combinatorics.

  • Anyone preparing for advanced courses in mathematics, statistics, or data science.

  • Individuals are interested in applications of probability and combinatorics in various fields.

Course Outcome:

By the end of this course, you will have a solid grasp of probability and combinatorics, enabling you to tackle more advanced coursework or apply these principles to real-world scenarios. You'll also be better prepared for careers that require strong analytical and problem-solving skills.

Goals

Fundamentals of Probability:

  • Understand the concept of probability and its importance in decision-making and risk assessment.

  • Learn about basic probability rules and axioms.

  • Explore different types of probability distributions, including discrete and continuous distributions.

  1. Combinatorial Mathematics:

    • Dive into combinatorial mathematics, focusing on counting techniques and permutations.

    • Study combinations, binomial coefficients, and the inclusion-exclusion principle.

    • Solve real-world problems using combinatorial methods.

  2. Applications in Various Fields:

    • Discover how probability and combinatorics are applied in fields such as finance, science, and gaming.

    • Gain insights into their role in data analysis and statistics.

    • Explore real-world examples and case studies.

  3. Problem-Solving and Exercises:

    • Engage in hands-on exercises and problem-solving sessions to reinforce your understanding.

    • Practice applying probability and combinatorics concepts to solve practical problems.

    • Challenge yourself with thought-provoking exercises to hone your skills.

  4. Interactive Learning Environment:

    • Benefit from an interactive and supportive online learning platform.

    • Access video lectures, quizzes, and assignments that cater to various learning styles.

    • Collaborate with fellow students and receive guidance from experienced instructors.

Prerequisites

  • This course assumes a basic understanding of algebra and mathematical concepts. No prior knowledge of probability or combinatorics is required.
Fundamentals Tools of Probability and Combinatorics

Curriculum

Check out the detailed breakdown of what’s inside the course

Unveiling Uncertainty: Exploring Probability Basics and Random Experiments

2 Lectures
  • play icon Unveiling Uncertainty: Exploring Probability Basics and Random Experiments 02:54 02:54
  • play icon Laying the Foundation: Understanding Sample Spaces and Events in Probability 03:38 03:38

Unlocking the World of Combinations and Permutations in Combinatorics

3 Lectures
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Data Analysis with Google Colab: Central Tendency & Probability

5 Lectures
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Simulating Randomness: Sampling from Distributions

5 Lectures
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Get Your Data Ready to Shine: Data Cleaning and Preprocessing Fundamentals

5 Lectures
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Instructor Details

AKHIL VYDYULA

AKHIL VYDYULA

Data Scientist | Data & Analytics Specialist | Entrepreneur

Hello, I'm Akhil, a Senior Data Scientist at PwC specializing in the Advisory Consulting practice with a focus on Data and Analytics.

My career journey has provided me with the opportunity to delve into various aspects of data analysis and modelling, particularly within the BFSI sector, where I've managed the full lifecycle of development and execution.


I possess a diverse skill set that includes data wrangling, feature engineering, algorithm development, and model implementation. My expertise lies in leveraging advanced data mining techniques, such as statistical analysis, hypothesis testing, regression analysis, and both unsupervised and supervised machine learning, to uncover valuable insights and drive data-informed decisions. I'm especially passionate about risk identification through decision models, and I've honed my skills in machine learning algorithms, data/text mining, and data visualization to tackle these challenges effectively.


Currently, I am deeply involved in an exciting Amazon cloud project, focusing on the end-to-end development of ETL processes. I write ETL code using PySpark/Spark SQL to extract data from S3 buckets, perform necessary transformations, and execute scripts via EMR services. The processed data is then loaded into Postgres SQL (RDS/Redshift) in full, incremental, and live modes. To streamline operations, I’ve automated this process by setting up jobs in Step Functions, which trigger EMR instances in a specified sequence and provide execution status notifications. These Step Functions are scheduled through EventBridge rules.


Moreover, I've extensively utilized AWS Glue to replicate source data from on-premises systems to raw-layer S3 buckets using AWS DMS services. One of my key strengths is understanding the intricacies of data and applying precise transformations to convert data from multiple tables into key-value pairs. I’ve also optimized stored procedures in Postgres SQL to efficiently perform second-level transformations, joining multiple tables and loading the data into final tables.


I am passionate about harnessing the power of data to generate actionable insights and improve business outcomes. If you share this passion or are interested in collaborating on data-driven projects, I would love to connect. Let’s explore the endless possibilities that data analytics can offer!

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