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4:33 AM
Q: $ax^2 + 2hxy + by^2 +2gx + 2fy+c = 0$ represents a point when $\Delta = 0$ and $h^2 - ab < 0$.

saniHow can I show that $ax^2 + 2hxy + by^2 +2gx + 2fy+c = 0$ represents a point when $\Delta = 0$ and $h^2 - ab < 0$. I know I can do it by completing the square. But it turns out to be too tedious. Can anyone help me ?

16 hours later…
8:42 PM
A new tag was created and added to 9 questions. MathOverflow has a tag called learning-roadmap, it has 14 questions.
Q: Roadmap to rigid cohomology

andresI am interested in the study of p-adic geometry. Unfortunately what I know is basic Algebraic geometry and basic number theory. To get an idea of the amount of material to study what could be a "roadmap" for reaching tools like rigid cohomology ? Thanks for the answers.

Q: Learning roadmap: 'combinatorial' probability

Jyotirmoy BhattacharyaI am about to finish working through Williams's Probability With Martingales. I have studied analysis up to the first five chapters of Folland's text but have not studied any combinatorics yet. It seems like 'combinatorial' probability topics like percolation, probability on graphs and networks,...

Q: Roadmap to SPDEs

SimonI'm trying to learn about the Kushner-Stratonovich-Pardoux equations in filtering theory. I'm familiar with Itô calculus at the level of Øksendal's book (but struggle with much of Karatzas and Shreve, for example). My PDE theory is pretty weak. I know about the Fokker-Planck equations, and that...

Q: Roadmap to Iwasawa Theory

JDivisionI haven’t found any posts on this, so I figured I would ask. Beyond learning basic algebra (rings, groups, fields) and complex analysis, what must one study if they want to start learning a good amount of iwasawa theory? In what sequence should they study this material?

Q: Learning roadmap to Topological Quantum Field Theories from a mathematics perspective

user90041I want to learn TQFT's and am looking for review articles or books. My mathematics knowledge is limited to one year of graduate course in Algebra (Groups,Rings,Fields,Categories, Modules and Homological Algebra), self study of Geometry (Manifolds, Differential Geometry, Riemannian Metrics, Curvat...

Q: Learning Roadmap for Borel - Weil - Bott Theorem

user38268Next semester I may study a course where the ultimate goal is to get to the Borel - Weil - Bott (BWB) Theorem, if not at least try to understand it in the case that we have $G = \text{SL}_n$. I have studied some representation theory of Lie groups from Brian Hall's book Lie groups, Lie algebras ...

Q: Roadmap to Modern Research in Partial Differential Equations

user659078Let me start off with a description of my background. I am an undergraduate student, with some background in real analysis (Rudin, Principles of Mathematical Analysis), measure theory (Royden, Real Analysis: Parts I and III) and a little functional analysis (first five chapters of Rudin's 'Real a...

Q: Learning Roadmap for Algebraic Topology

ArsenalerI am now considering about studying algebraic topology. There are a lot of books about it, and I want to choose the most comprehensive book among them. I have a solid background in Abstract Algebra, and also have knowledge on Homological Algebra(in fact I am now study Tor and Ext functors). But m...

Q: Suggestions for a learning roadmap for universal algebra?

user89I think a useful combination of resources for universal algebra would ideally, when taken together: Provide ample motivation behind the various developments in the field. Either provide powerful intuitions, or avoid them altogether, in an effort to not cripple the learner's imagination. Provide...

Posts where the tag was added/removed (including the editors): data.stackexchange.com/math/query/1105163/… data.stackexchange.com/math/query/1038474/…
Q: Should the main site have a 'roadmap' tag?

Descartes Before the HorseI think a new tag roadmap should be made on the main site. (Actually, I already made it and tagged some example posts, which can be found here.) The 'roadmap' tag is meant to classify those questions which seek a comprehensive, dependency-graph-like list of resources/references/topics one must st...


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