Welcome to the *Math Online* Wikidot page! Here you are able to browse through a wide range of mathematics topics and enhance your understanding of mathematics! The pages on Math Online provide many examples and visuals to enhance learning while still delivering the important key concepts to understanding undergraduate mathematics. **Be careful though! All of these notes have been written by me throughout my undergraduate and graduate degree, so many pages contain typos, errors, or are not written in the most suitable manner, so use these notes at your own risk!**

# Directory of Subjects

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## Recently Added Pages

Page | Date created |
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Finite-Dimensional Vector Spaces Have a Unique LC & H Topology | 04 Mar 2020 19:58 |

The Dual Base for E* of a Finite-Dimensional Vector Space E | 04 Mar 2020 19:45 |

The Polar of an Intersection of σ(E, F)-Closed Absolutely Convex Sets | 04 Mar 2020 18:59 |

Hausdorff LCTVS: A°° (in E) is the Closed Absolutely Convex Hull of A | 04 Mar 2020 18:42 |

A°° is the σ(G, F)-Closed Absolutely Convex Hull of A | 04 Mar 2020 18:02 |

If E ⊆ G ⊆ F* and (E, F) is a Dual Pair, A ⊆ A°° | 04 Mar 2020 17:35 |

The Bipolar of a Set | 04 Mar 2020 17:17 |

The Polar Criterion for Equicontinuity of a Set of Linear Forms | 04 Mar 2020 17:02 |

The Polar of a Subspace | 04 Mar 2020 16:34 |

The Polar of a Set | 04 Mar 2020 16:21 |

Topologies of the Dual Pair (E, F) | 11 Feb 2020 19:18 |

The Topological Dual of E Equipped with σ(E, F) is F | 11 Feb 2020 18:31 |

The Weak Topology on E Determined by F | 11 Feb 2020 18:09 |

Dual Pairs of Vector Spaces | 11 Feb 2020 17:59 |

Corollaries to the Hahn-Banach Theorem for Vector Spaces 1 | 03 Feb 2020 02:35 |

## Math Online News

MAY 1ST, 2019: Sorry for being away for over half a year! I have been quite busy with my own personal studies. I plan to continue to add pages on a slightly more consistent basis from now on, but not as frequently as I used to due to time constraints. I have received a few very nice comments from you guys saying that you appreciate the site, and I'm really glad for it! I created this site 6 years ago when I was starting my undergraduate degree as a way for me to keep my notes and solved problems in case I needed or wanted to relearn them down the road. I had no idea that so many people would enjoy reading my notes and problems (although a lot of them are error-riden!) Thank you all for your kind words and I'm glad you're enjoying the site. Also, I have corrected a lot of the errors posted on the errors page. Many reported errors haven't been fixed yet (and I probably won't be able to correct them at this point in time unless I relearn the material from scratch, which isn't an option for me at the present time unfortunately). Regardless, thank you all who have reported errors, and I'm sorry if any reported error hasn't been fixed by me yet. I hope to get around to it… some day. Keep your eyes keen though, as a large part of math is questioning things that don't look quite right =)! |

AUGUST 6th, 2018: Math Online just reached 3000 pages of content :D! |

JULY 30th, 2018: The Abstract Algebra section is undergoing clean up. A bunch of pages have been reorganized and/or modernized! Additional topics have also been added. |

MAY 3rd, 2018: The Topology section will be undergoing some cleaning up for the next couple of weeks. |

JANUARY 8th, 2017: Happy New Years! Tons of additional math pages will be added this year! |

JANUARY 10th, 2016: The Number Theory section is almost fully overhauled! About 80% of the pages have been cleaned up with various additions/removals, improved wording and notation, etc… |

DECEMBER 28th, 2015: The colours of the hub pages have been modified. |

NOVEMBER 10th, 2015: I've modified the hub page links to be more colourful! |

SEPTEMBER 28th, 2015: Math Online now has over 1500 pages of content! Woo :)! |

SEPTEMBER 2ND, 2015: Just changed the Math Online favicon to a modern and sleek $*$ operation symbol! |

SEPTEMBER 1ST, 2015: Lots of updates! All of the hub pages (except for Number Theory) are condensed to reduce vertical scrolling. A lot of the main graphics have also changed including the icons representing Linear Algebra and Graph Theory. Incorrectly sized headings on hub pages have also been fixed! |

AUGUST 28TH, 2015: The "Abstract Algebra" section was created a few days ago and the front page has received some aesthetic changes including colour-coded hub pages. The background also changes upon refresh! The Number Theory section will also be getting some edits over the next week as most of the Number Theory pages are low quality in comparison with the rest of the site. |

AUGUST 17TH, 2015: Over the last 9 days I have worked extensively on the new, Combinatorics page! For the following week I will be finally working on neatening the Graph Theory pages, adding more pages to the combinatorics section, and perhaps starting on a new section or working on an existing section. |

APRIL 4TH, 2015: Math Online officially has over 1000 pages of content available! Can't wait for the next 1000 pages of content! |

MARCH 11TH, 2015: I have cleaned up the Differential Equations page and made it more user friendly. I have also done a little cleaning on the Linear Algebra pages. I plan to update the Graph Theory and Number Theory pages in May as their styles are a little outdated with the new standards that have been in place on the site. I have also added a new search feature on the main page of the site! |

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Math Online has over 3165 pages of content!