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Excelling in GCSE Religious Studies! At GLA Tutors, we are dedicated to helping students succeed in their GCSE Religious Studies examinations. Our experienced tutors are passionate about the subject and committed to providing comprehensive support aligned with the AQA examination board's specification. Let's explore the breakdown of the AQA GCSE Religious Studies specification: Paper 1: The Study of Religions: Beliefs and Teachings This paper focuses on the study of two religions, such as Christianity and Islam. Our tutors will guide students through the fundamental beliefs, teachings, and practices of these religions. We delve into topics like the nature of God, religious texts, worship, and the impact of religion on individuals and society. Through engaging discussions and thought-provoking exercises, we help students develop a deep understanding of religious beliefs. Paper 2: Thematic Studies This paper explores ethical and philosophical issues, as well as the influence of religion in the modern world. Our tutors will delve into topics like crime and punishment, human rights, life and death, and religion and society. We provide in-depth analysis, case studies, and perspectives from different religious traditions to enable students to critically examine these issues. We also emphasise the development of strong argumentation and evaluation skills. Paper 3: Study of Religion: Textual Studies In this paper, students will explore religious texts and their significance. Our tutors will guide students through the study of sacred texts, such as the Bible or the Qur'an. We help students analyse and interpret these texts, understand their historical and cultural context, and explore their relevance in contemporary society. We provide comprehensive guidance on textual analysis and the application of religious teachings to real-life situations. At GLA Tutors, we foster a supportive and inclusive learning environment, where students can explore and deepen their understanding of religious studies. Our tutors provide personalised one-on-one sessions, group discussions, and access to a range of learning resources to cater to each student's unique needs. Beyond the specification, we encourage critical thinking, empathy, and open-mindedness, enabling students to engage with complex ethical and philosophical questions. We also focus on developing strong exam techniques, essay writing skills, and effective revision strategies to maximize exam success. Join us at GLA Tutors and embark on a transformative journey in GCSE Religious Studies. Our tutors are here to guide you towards academic excellence, a deep appreciation for religious diversity, and the ability to apply religious teachings to real-world contexts. Feel free to explore our website for more information or reach out to us with any questions you may have. Let's embark on this enriching educational adventure together! We can provide assistance for everything you need to prepare students for exams, including: past papers, mark schemes and examiners’ reports specimen papers and mark schemes for new courses exemplar student answers with examiner commentaries high quality revision guides

Duration 3 Days 18 CPD hours This course is intended for This course is geared for Python-experienced attendees who wish to be equipped with the skills you need to use pandas to ensure the veracity of your data, visualize it for effective decision-making, and reliably reproduce analyses across multiple datasets. Overview Working in a hands-on learning environment, guided by our expert team, attendees will learn to: Understand how data analysts and scientists gather and analyze data Perform data analysis and data wrangling using Python Combine, group, and aggregate data from multiple sources Create data visualizations with pandas, matplotlib, and seaborn Apply machine learning (ML) algorithms to identify patterns and make predictions Use Python data science libraries to analyze real-world datasets Use pandas to solve common data representation and analysis problems Build Python scripts, modules, and packages for reusable analysis code Perform efficient data analysis and manipulation tasks using pandas Apply pandas to different real-world domains with the help of step-by-step demonstrations Get accustomed to using pandas as an effective data exploration tool. Data analysis has become a necessary skill in a variety of domains where knowing how to work with data and extract insights can generate significant value. Geared for data team members with incoming Python scripting experience, Hands-On Data Analysis with Pandas will show you how to analyze your data, get started with machine learning, and work effectively with Python libraries often used for data science, such as pandas, NumPy, matplotlib, seaborn, and scikit-learn. Using real-world datasets, you will learn how to use the powerful pandas library to perform data wrangling to reshape, clean, and aggregate your data. Then, you will be able to conduct exploratory data analysis by calculating summary statistics and visualizing the data to find patterns. In the concluding lessons, you will explore some applications of anomaly detection, regression, clustering, and classification using scikit-learn to make predictions based on past data. Students will leave the course armed with the skills required to use pandas to ensure the veracity of their data, visualize it for effective decision-making, and reliably reproduce analyses across multiple datasets. Introduction to Data Analysis Fundamentals of data analysis Statistical foundations Setting up a virtual environment Working with Pandas DataFrames Pandas data structures Bringing data into a pandas DataFrame Inspecting a DataFrame object Grabbing subsets of the data Adding and removing data Data Wrangling with Pandas What is data wrangling? Collecting temperature data Cleaning up the data Restructuring the data Handling duplicate, missing, or invalid data Aggregating Pandas DataFrames Database-style operations on DataFrames DataFrame operations Aggregations with pandas and numpy Time series Visualizing Data with Pandas and Matplotlib An introduction to matplotlib Plotting with pandas The pandas.plotting subpackage Plotting with Seaborn and Customization Techniques Utilizing seaborn for advanced plotting Formatting Customizing visualizations Financial Analysis - Bitcoin and the Stock Market Building a Python package Data extraction with pandas Exploratory data analysis Technical analysis of financial instruments Modeling performance Rule-Based Anomaly Detection Simulating login attempts Exploratory data analysis Rule-based anomaly detection Getting Started with Machine Learning in Python Learning the lingo Exploratory data analysis Preprocessing data Clustering Regression Classification Making Better Predictions - Optimizing Models Hyperparameter tuning with grid search Feature engineering Ensemble methods Inspecting classification prediction confidence Addressing class imbalance Regularization Machine Learning Anomaly Detection Exploring the data Unsupervised methods Supervised methods Online learning The Road Ahead Data resources Practicing working with data Python practice

Duration 4 Days 24 CPD hours This course is intended for This class is intended for experienced developers who are responsible for managing big data transformations including: Extracting, loading, transforming, cleaning, and validating data. Designing pipelines and architectures for data processing. Creating and maintaining machine learning and statistical models. Querying datasets, visualizing query results and creating reports Overview Design and build data processing systems on Google Cloud Platform. Leverage unstructured data using Spark and ML APIs on Cloud Dataproc. Process batch and streaming data by implementing autoscaling data pipelines on Cloud Dataflow. Derive business insights from extremely large datasets using Google BigQuery. Train, evaluate and predict using machine learning models using TensorFlow and Cloud ML. Enable instant insights from streaming data Get hands-on experience with designing and building data processing systems on Google Cloud. This course uses lectures, demos, and hand-on labs to show you how to design data processing systems, build end-to-end data pipelines, analyze data, and implement machine learning. This course covers structured, unstructured, and streaming data. Introduction to Data Engineering Explore the role of a data engineer. Analyze data engineering challenges. Intro to BigQuery. Data Lakes and Data Warehouses. Demo: Federated Queries with BigQuery. Transactional Databases vs Data Warehouses. Website Demo: Finding PII in your dataset with DLP API. Partner effectively with other data teams. Manage data access and governance. Build production-ready pipelines. Review GCP customer case study. Lab: Analyzing Data with BigQuery. Building a Data Lake Introduction to Data Lakes. Data Storage and ETL options on GCP. Building a Data Lake using Cloud Storage. Optional Demo: Optimizing cost with Google Cloud Storage classes and Cloud Functions. Securing Cloud Storage. Storing All Sorts of Data Types. Video Demo: Running federated queries on Parquet and ORC files in BigQuery. Cloud SQL as a relational Data Lake. Lab: Loading Taxi Data into Cloud SQL. Building a Data Warehouse The modern data warehouse. Intro to BigQuery. Demo: Query TB+ of data in seconds. Getting Started. Loading Data. Video Demo: Querying Cloud SQL from BigQuery. Lab: Loading Data into BigQuery. Exploring Schemas. Demo: Exploring BigQuery Public Datasets with SQL using INFORMATION_SCHEMA. Schema Design. Nested and Repeated Fields. Demo: Nested and repeated fields in BigQuery. Lab: Working with JSON and Array data in BigQuery. Optimizing with Partitioning and Clustering. Demo: Partitioned and Clustered Tables in BigQuery. Preview: Transforming Batch and Streaming Data. Introduction to Building Batch Data Pipelines EL, ELT, ETL. Quality considerations. How to carry out operations in BigQuery. Demo: ELT to improve data quality in BigQuery. Shortcomings. ETL to solve data quality issues. Executing Spark on Cloud Dataproc The Hadoop ecosystem. Running Hadoop on Cloud Dataproc. GCS instead of HDFS. Optimizing Dataproc. Lab: Running Apache Spark jobs on Cloud Dataproc. Serverless Data Processing with Cloud Dataflow Cloud Dataflow. Why customers value Dataflow. Dataflow Pipelines. Lab: A Simple Dataflow Pipeline (Python/Java). Lab: MapReduce in Dataflow (Python/Java). Lab: Side Inputs (Python/Java). Dataflow Templates. Dataflow SQL. Manage Data Pipelines with Cloud Data Fusion and Cloud Composer Building Batch Data Pipelines visually with Cloud Data Fusion. Components. UI Overview. Building a Pipeline. Exploring Data using Wrangler. Lab: Building and executing a pipeline graph in Cloud Data Fusion. Orchestrating work between GCP services with Cloud Composer. Apache Airflow Environment. DAGs and Operators. Workflow Scheduling. Optional Long Demo: Event-triggered Loading of data with Cloud Composer, Cloud Functions, Cloud Storage, and BigQuery. Monitoring and Logging. Lab: An Introduction to Cloud Composer. Introduction to Processing Streaming Data Processing Streaming Data. Serverless Messaging with Cloud Pub/Sub Cloud Pub/Sub. Lab: Publish Streaming Data into Pub/Sub. Cloud Dataflow Streaming Features Cloud Dataflow Streaming Features. Lab: Streaming Data Pipelines. High-Throughput BigQuery and Bigtable Streaming Features BigQuery Streaming Features. Lab: Streaming Analytics and Dashboards. Cloud Bigtable. Lab: Streaming Data Pipelines into Bigtable. Advanced BigQuery Functionality and Performance Analytic Window Functions. Using With Clauses. GIS Functions. Demo: Mapping Fastest Growing Zip Codes with BigQuery GeoViz. Performance Considerations. Lab: Optimizing your BigQuery Queries for Performance. Optional Lab: Creating Date-Partitioned Tables in BigQuery. Introduction to Analytics and AI What is AI?. From Ad-hoc Data Analysis to Data Driven Decisions. Options for ML models on GCP. Prebuilt ML model APIs for Unstructured Data Unstructured Data is Hard. ML APIs for Enriching Data. Lab: Using the Natural Language API to Classify Unstructured Text. Big Data Analytics with Cloud AI Platform Notebooks What's a Notebook. BigQuery Magic and Ties to Pandas. Lab: BigQuery in Jupyter Labs on AI Platform. Production ML Pipelines with Kubeflow Ways to do ML on GCP. Kubeflow. AI Hub. Lab: Running AI models on Kubeflow. Custom Model building with SQL in BigQuery ML BigQuery ML for Quick Model Building. Demo: Train a model with BigQuery ML to predict NYC taxi fares. Supported Models. Lab Option 1: Predict Bike Trip Duration with a Regression Model in BQML. Lab Option 2: Movie Recommendations in BigQuery ML. Custom Model building with Cloud AutoML Why Auto ML? Auto ML Vision. Auto ML NLP. Auto ML Tables.

Duration 2 Days 12 CPD hours This course is intended for This course is aimed at anyone currently working with data who is interested in using data visualisation to more effectively communicate their results. Overview At completion, delegates will understand how data visualisations can be best used to communicate actionable insights from data and be competent with the tools required to do it. Visualising data, and analytics results, is one of the most effective ways to achieve this. This course will cover the theory of data visualisation along with practical skills for creating compelling visualisations from data. Course Outline The use of analytics, statistics and data science in business has grown massively in recent years. Harnessing the power of data is opening actionable insights in diverse industries from banking to horse breeding. The companies doing this most successfully understand that using sophisticated analytics approaches to unlock insights from data is only half the job. Communicating these insights to all of the different parts of an organisation is just as important as doing the actual analysis. Visualising data, and analytics results, is one of the most effective ways to achieve this. This course will cover the theory of data visualisation along with practical skills for creating compelling visualisations from data. To attend this course delegates should be competent in the use of data analysis tools such as reporting tools, spreadsheet software or business intelligence tools. The course will explore the following topics through a series of interactive workshop sessions: Fundamentals of data visualisation Data characteristics & dimensions Mapping visual encodings to data dimensions Colour theory Graphical perception & communication Interaction design Visualisation different characteristics of data: trends, comparisons, correlations, maps, networks, hierarchies, text Designing effective dashboards

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Duration 2 Days 12 CPD hours This course is intended for New users of IBM SPSS Statistics Users who want to refresh their knowledge about IBM SPSS Statistics Anyone who is considering purchasing IBM SPSS Statistics Overview Introduction to IBM SPSS Statistics Review basic concepts in IBM SPSS Statistics Identify the steps in the research process Review basic analyses Use Help Reading data and defining metadata Overview of data sources Read from text files Read data from Microsoft Excel Read data from databases Define variable properties Selecting cases for analyses Select cases for analyses Run analyses for groups Apply report authoring styles Transforming variables Compute variables Recode values of categorical and scale variables Create a numeric variable from a string variable Using functions to transform variables Use statistical functions Use logical functions Use missing value functions Use conversion functions Use system variables Use the Date and Time Wizard Setting the unit of analysis Remove duplicate cases Create aggregate datasets Restructure datasets Merging data files Add cases from one dataset to another Add variables from one dataset to another Enrich a dataset with aggregated information Summarizing individual variables Define levels of measurement Summarizing categorical variables Summarizing scale variables Describing the relationship between variables Choose the appropriate procedure Summarize the relationship between categorical variables Summarize the relationship between a scale and a categorical variable Creating presentation ready tables with Custom Tables Identify table layouts Create tables for variables with shared categories Create tables for multiple response questions Customizing pivot tables Perform Automated Output Modification Customize pivot tables Use table templates Export pivot tables to other applications Working with syntax Use syntax to automate analyses Create, edit, and run syntax Shortcuts in the Syntax Editor Controlling the IBM SPSS Statistics environment Set options for output Set options for variables display Set options for default working folders This course guides students through the fundamentals of using IBM SPSS Statistics for typical data analysis. Students will learn the basics of reading data, data definition, data modification, data analysis, and presentation of analytical results. In addition to the fundamentals, students will learn shortcuts that will help them save time. This course uses the IBM SPSS Statistics Base; one section presents an add-on module, IBM SPSS Custom Tables. Introduction to IBM SPSS Statistics Review basic concepts in IBM SPSS Statistics Identify the steps in the research process Review basic analyses Use Help Reading data and defining metadata Overview of data sources Read from text files Read data from Microsoft Excel Read data from databases Define variable properties Selecting cases for analyses Select cases for analyses Run analyses for groups Apply report authoring styles Transforming variables Compute variables Recode values of categorical and scale variables Create a numeric variable from a string variable Using functions to transform variables Use statistical functions Use logical functions Use missing value functions Use conversion functions Use system variables Use the Date and Time Wizard Setting the unit of analysis Remove duplicate cases Create aggregate datasets Restructure datasets Merging data files Add cases from one dataset to another Add variables from one dataset to another Enrich a dataset with aggregated information Summarizing individual variables Define levels of measurement Summarizing categorical variables Summarizing scale variables Describing the relationship between variables Choose the appropriate procedure Summarize the relationship between categorical variables Summarize the relationship between a scale and a categorical variable Creating presentation ready tables with Custom Tables Identify table layouts Create tables for variables with shared categories Create tables for multiple response questions Customizing pivot tables Perform Automated Output Modification Customize pivot tables Use table templates Export pivot tables to other applications Working with syntax Use syntax to automate analyses Create, edit, and run syntax Shortcuts in the Syntax Editor Controlling the IBM SPSS Statistics environment Set options for output Set options for variables display Set options for default working folders Additional course details: Nexus Humans 0G53BG IBM SPSS Statistics Essentials (V26) training program is a workshop that presents an invigorating mix of sessions, lessons, and masterclasses meticulously crafted to propel your learning expedition forward. This immersive bootcamp-style experience boasts interactive lectures, hands-on labs, and collaborative hackathons, all strategically designed to fortify fundamental concepts. Guided by seasoned coaches, each session offers priceless insights and practical skills crucial for honing your expertise. Whether you're stepping into the realm of professional skills or a seasoned professional, this comprehensive course ensures you're equipped with the knowledge and prowess necessary for success. While we feel this is the best course for the 0G53BG IBM SPSS Statistics Essentials (V26) course and one of our Top 10 we encourage you to read the course outline to make sure it is the right content for you. Additionally, private sessions, closed classes or dedicated events are available both live online and at our training centres in Dublin and London, as well as at your offices anywhere in the UK, Ireland or across EMEA.

Duration 2 Days 12 CPD hours This course is intended for This course is suited to marketeers, business analysts, and researchers who are interested in increasing their statistical knowledge. Overview After attending this course, delegates will understand how statistics can be used to provide valuable insight into their business, and be able to apply statistical methods to solve business problems. On returning to work delegates will immediately be able to make a difference to the way that their organisations make decisions. This course covers the statistical methods that analysts need to move from simple reporting on business problems to extracting insight to solve business problems. Course Outline The course will explore the following topics through a series of lectures and workshops: Summary statistics for both continuous data and categorical data Using and reporting confidence intervals Using hypothesis tests to answer business questions Using correlations to explore data relationships Simple prediction models Analysing categorical data Additional course details: Nexus Humans Data-driven Business Using Statistical Analysis training program is a workshop that presents an invigorating mix of sessions, lessons, and masterclasses meticulously crafted to propel your learning expedition forward. This immersive bootcamp-style experience boasts interactive lectures, hands-on labs, and collaborative hackathons, all strategically designed to fortify fundamental concepts. Guided by seasoned coaches, each session offers priceless insights and practical skills crucial for honing your expertise. Whether you're stepping into the realm of professional skills or a seasoned professional, this comprehensive course ensures you're equipped with the knowledge and prowess necessary for success. While we feel this is the best course for the Data-driven Business Using Statistical Analysis course and one of our Top 10 we encourage you to read the course outline to make sure it is the right content for you. Additionally, private sessions, closed classes or dedicated events are available both live online and at our training centres in Dublin and London, as well as at your offices anywhere in the UK, Ireland or across EMEA.

Excel in IGCSE Mathematics with our CPD Accredited course. Develop problem-solving skills, learn key concepts, and gain exam preparation strategies.

Number Theory Basics is yet another 'Teacher's Choice' course from Teachers Training for a complete understanding of the fundamental topics. You are also entitled to exclusive tutor support and a professional CPD-accredited certificate in addition to the special discounted price for a limited time. Just like all our courses, this Number Theory Basics and its curriculum have also been designed by expert teachers so that teachers of tomorrow can learn from the best and equip themselves with all the necessary skills. Consisting of several modules, the course teaches you everything you need to succeed in this profession. The course can be studied part-time. You can become accredited within 9 hours studying at your own pace. Your qualification will be recognised and can be checked for validity on our dedicated website. Why Choose Teachers Training Some of our website features are: This is a dedicated website for teaching 24/7 tutor support Interactive Content Affordable price Courses accredited by the UK's top awarding bodies 100% online Flexible deadline Entry Requirements No formal entry requirements. You need to have: Passion for learning A good understanding of the English language Be motivated and hard-working Over the age of 16. Certification CPD Certification from The Teachers Training Successfully completing the MCQ exam of this course qualifies you for a CPD-accredited certificate from The Teachers Training. You will be eligible for both PDF copy and hard copy of the certificate to showcase your achievement however you wish. You can get your digital certificate (PDF) for £4.99 only Hard copy certificates are also available, and you can get one for only £10.99 You can get both PDF and Hard copy certificates for just £12.99! The certificate will add significant weight to your CV and will give you a competitive advantage when applying for jobs. Introduction What is Number Theory 00:08:00 Basics of Number Theory Number Theory 00:07:00 Number Sets 00:09:00 Number Patterns 00:10:00 Even & Odd Numbers 00:11:00 Number Properties 00:10:00 Proofs 00:11:00 Number Bases Number Bases 00:12:00 Binary Base 00:12:00 Binary Arithmetics 00:15:00 Hexadecimal Base 00:13:00 Hexadecimal Arithmetics 00:14:00 Factorials Factorial 00:05:00 Double Factorial 00:09:00 Super Factorial 00:03:00 Exponential Factorial 00:03:00 Factorion 00:05:00 Stirling's Formula 00:03:00 Number of Digits 00:03:00 Divisibility Divisibility 00:07:00 Divisibility Rules 00:04:00 Euclidean Division Theorem 00:08:00 GCD & LCM 00:11:00 Bézout's Identity 00:08:00 Perfect Numbers 00:04:00 Practical Numbers 00:05:00 Amicable Numbers 00:04:00 Fibonacci Sequence 00:09:00 Tribonacci Sequence 00:05:00 Golden Ratio 00:11:00 Primes Prime Numbers 00:09:00 Fundamental Theorem of Arithmetics (FTA) 00:10:00 Almost Primes 00:07:00 Prime Powers 00:02:00 Factorial Prime 00:03:00 Euclid's Theorems 00:09:00 The Prime Number Theorem 00:04:00 Unsolved Problems 00:06:00 Number Empire 00:07:00 Modular Arithmetic Modular Arithmetics 00:09:00 Congruence 00:13:00 Congruence Class 00:12:00 Residue Systems 00:04:00 Quadratic Residues 00:04:00 Modular Operations 00:06:00 Inverses 00:07:00 Modular Exponentiation 00:10:00 Wilson's Theorem 00:05:00 Chinese Remainder Theorem 00:09:00 Fermat's Little Theorem 00:05:00 Euler's Totient Function 00:07:00 Euler-Fermat Theorem 00:04:00 Continued Fractions Continued Fractions 00:08:00 Negative Continued Fractions 00:11:00 Finite Continued Fractions 00:14:00 Infinite Continued Fractions 00:17:00 Periodic Continued Fractions 00:10:00 Convergent 00:12:00 Cryptography Cryptography 00:09:00 Early Ciphers 00:11:00 Public Key Cryptography 00:13:00 RSA Encryption 00:11:00 Diffie-Hellman Protocol 00:04:00 Resources Resource - An Introduction to Number Theory 00:05:00

Graph Theory Basics is yet another 'Teacher's Choice' course from Teachers Training for a complete understanding of the fundamental topics. You are also entitled to exclusive tutor support and a professional CPD-accredited certificate in addition to the special discounted price for a limited time. Just like all our courses, this Graph Theory Basics and its curriculum have also been designed by expert teachers so that teachers of tomorrow can learn from the best and equip themselves with all the necessary skills. Consisting of several modules, the course teaches you everything you need to succeed in this profession. The course can be studied part-time. You can become accredited within 10 hours studying at your own pace. Your qualification will be recognised and can be checked for validity on our dedicated website. Why Choose Teachers Training Some of our website features are: This is a dedicated website for teaching 24/7 tutor support Interactive Content Affordable price Courses accredited by the UK's top awarding bodies 100% online Flexible deadline Entry Requirements No formal entry requirements. You need to have: Passion for learning A good understanding of the English language Be motivated and hard-working Over the age of 16. Certification Successfully completing the MCQ exam of this course qualifies you for a CPD-accredited certificate from The Teachers Training. You will be eligible for both PDF copy and hard copy of the certificate to showcase your achievement however you wish. You can get your digital certificate (PDF) for £4.99 only Hard copy certificates are also available, and you can get one for only £10.99 You can get both PDF and Hard copy certificates for just £12.99! The certificate will add significant weight to your CV and will give you a competitive advantage when applying for jobs. Course Promo Graph Theory Promo 00:02:00 Module 01: Supplements Textbook Recommendations 00:02:00 Tools and Softwares 00:05:00 Sets 00:09:00 Number Sets 00:10:00 Parity 00:12:00 Terminologies 00:07:00 Module 02: Fundamentals Introduction 00:03:00 Graphs 00:11:00 Subgraphs 00:09:00 Degree 00:10:00 Sum of Degrees of Vertices Theorem 00:23:00 Adjacency and Incidence 00:09:00 Adjacency Matrix 00:16:00 Incidence Matrix 00:08:00 Isomorphism 00:08:00 Module 03: Paths Introduction 00:01:00 Walks, Trails, Paths, and Circuits 00:13:00 Examples 00:10:00 Eccentricity, Diameter, and Radius 00:07:00 Connectedness 00:20:00 Euler Trails and Circuits 00:18:00 Fleury's Algorithm 00:10:00 Hamiltonian Paths and Circuits 00:06:00 Ore's Theorem 00:14:00 Dirac's Theorem 00:06:00 The Shortest Path Problem 00:16:00 Module 04: Graph Types Introduction 00:01:00 Trivial, Null and Simple Graphs 00:10:00 Regular Graphs 00:10:00 Complete, Cycles and Cubic Graphs 00:10:00 Path, Wheel and Platonic Graphs 00:11:00 Bipartite Graphs 00:14:00 Module 05: Trees Introduction 00:01:00 Trees 00:14:00 Cayley's Theorem 00:03:00 Rooted Trees 00:10:00 Binary Trees 00:14:00 Binary Tree Traversals 00:18:00 Binary Expression Trees 00:09:00 Binary Search Trees 00:19:00 Spanning Trees 00:10:00 Forest 00:07:00 Module 06: Digraphs and Tournaments Introduction 00:01:00 Digraphs 00:12:00 Degree 00:09:00 Isomorphism 00:08:00 Adjacency Matrix 00:10:00 Incidence Matrix 00:05:00 Walks, Paths and Cycles 00:12:00 Connectedness 00:05:00 Tournaments 00:08:00 Module 07: Planar Graphs Introduction 00:01:00 Planar Graphs 00:10:00 Kuratowski's Theorem 00:14:00 Euler's Formula 00:10:00 Dual Graphs 00:11:00 Module 08: Graph Operations Introduction 00:01:00 Vertex and Edge Deletion & Addition 00:08:00 Cartesian Product 00:10:00 Graph Join and Transpose 00:04:00 Complement Graphs 00:05:00 Module 09: Graph Colourings Introduction 00:01:00 Vertex Colourings 00:05:00 Edge Colourings 00:09:00 Total Colourings 00:05:00