Muhammad Baig
Software Engineer & Mathematical Verifier
Muhammad Baig is a Software Engineer with a BSSE from the University of Sahiwal. He specializes in computational verification of mathematical equations, formulas, technical claims, and simulations, validating difficult SEO and information retrieval material by checking the logic in code.
Articles
How Web Crawlers Work: Seeds, URL Frontiers & Crawl Rate
A web crawler is a program that discovers pages on the web by fetching URLs, reading their HTML, extracting links, and adding those new links to a queue of pages to visit next. Tha...
What Is Information Retrieval? The Core Problem Every Search Engine Solves
Before search engines existed, IR researchers were solving the same core problem: how do you retrieve a relevant document from a large collection? This article defines the field's core concepts, precision, recall, relevance, and the recall-precision tradeoff, grounding every later topic in a rigorous framework that directly impact on your SEO Strategies and build your SEO thinking.
What Is the Vector Space Model? How Documents Become Numbers (and Why That Changes Everything)
The Vector Space Model represents documents and queries as mathematical vectors, making it possible to compare meaning through distance, angle, and weighted terms instead of simple keyword presence.
URL Discovery Explained: How Googlebot Finds Pages Through Links, Sitemaps, and Search Console
There is no central registry of web pages. Googlebot must continuously search for new and updated URLs on its own, using a process Google calls "URL discovery." There are three pathways into Googlebot's crawl frontier: following...
TF-IDF and BM25: The Mathematics of Keyword Relevance (And Why Repetition Stops Helping)
TF-IDF rewards terms that appear often in a document but rarely across the collection. BM25 (Best Match 25) extends this with diminishing returns on term frequency and document-length normalisation. Both remain the baseline every modern ranking model is measured against, and understanding them explains why keyword stuffing has never worked.
PageRank: How Brin and Page Replaced Word-Counting with Link-Counting
In 1998, Brin and Page made the leap from word-counting to link-counting. PageRank models a "random surfer" who clicks links with probability d (the damping factor, ~0.85) and occasionally jumps to a random page, the probability of ending up on any page is its rank score. A link from a high-PageRank page passes more authority than one from a low-PageRank page. This lesson covers the formula, convergence, and why this changed the web.
XML Sitemaps Explained: Schema, What to Include, What to Exclude, and Submission
An XML sitemap is a structured file that lists the URLs you want search engines to consider for crawling and indexing. It is a declaration of intent, not a command. Google's own documentation is explicit on this point: submitting a...
JavaScript SEO Explained: Googlebot's Two-Phase Crawl, SSR, and Dynamic Rendering
Googlebot can execute JavaScript. That fact alone has misled more development teams than almost any other statement in SEO. The ability to render is not the same as reliable, timely indexing. Googlebot crawls and renders in two...
MAP, MRR, and NDCG: The Metrics That Define What “Better Rankings” Actually Mean
Before you can improve a ranking system you need to measure it. Mean Average Precision (MAP) averages precision at every recall level. Mean Reciprocal Rank (MRR) measures how high the first correct result appears. Normalized Discounted Cumulative Gain (NDCG) accounts for graded relevance, a result in position 1 is worth more than position 5. These metrics drive every A/B test at Google and every LambdaRank training objective.
