Notes, summaries, assignments, exams, and problems for Other courses

Balancing Academic Goals and Personal Growth

First of all, I really need to vent tonight because trying to get in shape for the grueling UCSM admission exam while simultaneously pushing myself to improve my guitar skills is driving me a bit crazy lately. I had such a promising start when I first filled out my vision board, but honestly, some days I really struggle with motivation, and those two hours of daily study feel absolutely endless. Unsurprisingly, scrolling through my phone instead of opening my books is a bad habit that I can't seem to shake off easily, and there are nights when I just fail to stick to my goal perfectly. Nonetheless, I keep reminding myself that I need to set myself a challenge if I actually want to build a future that... Continue reading "Mastering Academic and Personal Goals: A Daily Routine" »

What is a Stream and its Classes in Java?

Introduction
A Stream is a sequence of data that flows between a program and an input/output device. Streams are used to perform input and output operations in Java. Java provides stream classes in the java.io package for reading and writing data. Streams simplify file handling and data communication.

Types of Streams

1. Input Stream

Used to read data from a source such as a file, keyboard, or network. Data flows from the source to the program.

2. Output Stream

Used to write data to a destination such as a file, screen, or network. Data flows from the program to the destination.

Various Stream Classes in Java

1. FileInputStream

Used to read data from a file. It reads data in byte format and is suitable for reading... Continue reading "Java Stream Classes and ArrayList Methods" »

Topic Modeling: LSI vs LDA

Latent Semantic Indexing (LSI)

Use LSI for semantic similarity, retrieval, short/sparse documents, and synonymy problems. It uses Singular Value Decomposition (SVD) to find latent concept axes from term-document co-occurrence. Concepts are mathematical directions, not clean probability-based topics. It is better when the goal is to “find similar documents.”

Latent Dirichlet Allocation (LDA)

Use LDA for discovering hidden themes and topic percentages. In this model, each document is a mixture of topics, and each topic is a distribution over words. It is better when the goal is to determine “what themes exist in this corpus?”

Key Distinction

• LSI finds latent concept dimensions.
• LDA explicitly models probabilistic topics.

Introduction

The Goods and Services Tax (GST) is a comprehensive indirect tax introduced on 1 July 2017. It replaced various Central and State indirect taxes, establishing a unified taxation system across India. GST aims to simplify taxation, increase transparency, and create a common national market.

Constitutional Aspects of GST

• Introduced via the Constitution (One Hundred and First Amendment) Act, 2016.
• Article 246A: Empowers Parliament and State Legislatures to enact GST laws.
• Article 269A: Governs GST on inter-State trade and commerce via IGST.
• Article 279A: Mandates the establishment of the GST Council.
• Strengthens cooperative federalism by balancing authority between the Centre and States.

Objectives and Key Features

• Unified Market: Achieving

GST Portal and GST Ecosystem

The GST system in India is a technology-driven tax regime. The entire functioning of GST—registration, return filing, tax payment, and refunds—is managed through a digital platform known as the GST Portal. This digital structure is supported by a wider GST Ecosystem, which includes various stakeholders such as taxpayers, government authorities, and service providers like GST Suvidha Providers (GSPs).

1. The GST Portal

Meaning

• The GST Portal is the official online platform for GST in India.
• It serves as the central hub for registration, return filing, tax payments, and refund applications.

Key Features

• Fully online and paperless system.
• Single platform for Central and State GST compliance.
• Facilitates GST registration

DFA vs NFA: Key Differences

Deterministic Finite Automata (DFA) vs Nondeterministic Finite Automata (NFA):

Deterministic Finite Automata (DFA)

• For each input symbol, only one transition is possible.
• No ε (epsilon) transitions are allowed.
• The transition function gives exactly one next state.
• Easier to implement in code.

Nondeterministic Finite Automata (NFA)

• For one input symbol, multiple transitions may be possible.
• ε-transitions may exist.
• The transition function gives zero, one, or many next states.
• Easier to design.

Pumping Lemma for Regular Languages

Statement

If L is a regular language, then there exists a pumping length p such that any string w in L with |w| ≥ p can be written as:

w = xyz

such that:

1. |xy| ≤ p
2. |y| > 0
3. xyⁿz ∈ L for all n ≥ 0

Primary

What is Software Engineering?

Software Engineering is the application of engineering principles, methods, and tools to the design, development, testing, deployment, operation, and maintenance of software systems in a systematic, disciplined, and measurable way.

Software Process Flows

A software process defines the approach used to develop a system. Common process flows include:

• Linear/Sequential: Activities are performed one after another in a fixed order. Each phase must be completed before the next begins.
• Iterative: The development process is repeated in cycles. Each iteration improves the software based on feedback.
• Evolutionary: The system is developed in versions or increments, where each version adds new features and improves the previous

The British administration in Manipur began after the Anglo-Manipur War of 1891. Although Manipur was not directly merged into British India, the British established strong political control over the state. They introduced administrative reforms, modern institutions, and economic changes, but their rule also weakened the traditional political system and reduced the sovereignty of the Manipuri monarchy.

Establishment of British Control

After defeating Manipur in 1891, the British executed several Manipuri leaders, including Tikendrajit and Thangal General. A minor king, Churachand Singh, was placed on the throne under British supervision. Real power remained in the hands of the British Political Agent. Thus, Manipur became a princely state under... Continue reading "British Rule in Manipur: History and Political Impact" »

Net Present Value and Cash Flows

The Net Present Value (NPV) formula is the sum of cash flows discounted by appropriate interest rates in future time periods. Free Cash Flows (FCF) are not simply profit, as non-cash assets exist, whilst FCF is equal to Cash From Operations (CFO) minus Capital Expenditure (CAPEX) minus the change in working capital (if included). Working capital is equal to current assets (e.g., accounts receivable) minus current liabilities (accounts payable). Investments in working capital are cash outflows, just like an investment in CAPEX. NPV only concerns cash because of the time value of money (cash can be reinvested to make more earnings, making a future £1 worth less than a present £1). Net income in year t is earnings... Continue reading "Corporate Finance: Valuation, Capital Structure, and M&A" »

Royal Albert Hall

The Royal Albert Hall was built in memory of Prince Albert and is closely related to art, music, and education. It reflects the Victorian belief that culture and knowledge could improve society, making it a symbol of Victorian culture, education, and progress.

St Pancras Station

St Pancras Station is one of the best examples of the Industrial Revolution. It represents technological progress and innovation through the use of iron and glass. The railway connected cities, encouraged trade and economic growth, and combined Gothic Revival architecture with modern engineering.

Oxford Museum of Natural History

The Oxford Museum of Natural History reflects Victorian interest in science, education, and discovery. It is associated with important... Continue reading "Victorian Architecture: Symbols of Progress and Power" »