Groupprops:Guided tour for beginners
Whom this guided tour is for
This guided tour is intended for beginners, viz people who:
- Are new to group theory, and have not yet seen (or have freshly seen) the definition and notion of group
- Are from disciplines related to mathematics wherein they encounter groups, but have had little formal training
- Have studied group theory long ago and would like to revise the basics
How to use the guided tour
The guided tour is organized in ten parts, and each part contains a series of pages that are meant to be navigated in the specified order. Each part of the guided tour contains about 5-10 pages, and on each page, there are links to the previous and next page.
In accordance with the principles of instructional design, we begin each part of the guided tour by stating the prerequisites of the part, as well as the goals that we seek to achieve in the given part. At the end of the part, we review what has been covered, by a series of bullet points, problems, and other confidence aggregators.
Each part usually begins with some definitions, then states some facts, and sometimes alternates between stating definitions and facts. Towards the end of the part, there may be one or more survey article. The survey article consolidates stuff that has been seen in the part, exploring the underlying motivation and addressing possible sources of confusion.
Thus, it is important, particularly for first-time readers, to follow the definitions, as well as the facts, and wait till the end of the part to get a reasonably complete picture of what's happened in the part.
For first-time readers not following any other reference
It's possible to go through this guided tour passively, i.e., without using paper and pencil. However, such an approach is not the most beneficial if you want to extract the most from the tour.
Here's a suggested approach to go about the guided tour:
- Keep a paper and pencil handy
- At the beginning of each part, make sure you have a reasonable understanding of the prerequisites for that part, and go through the goals, possibly making a note of them
- For many pages, you'll see a box on top listing prerequisites for the page, typically involving previous pages in the tour. If you don't know these prerequisites, revisit those pages. If you think you know the prerequisites, take a moment to recall them, and hold them in the mind's eye.
- For each page, you'll see, in the box, a WHAT YOU NEED TO DO. This tells you how you're supposed to go about reading the page. For instance, for a definition page, you're typically expected to go through all the equivalent definitions, and understand what they say. In some cases, you may be asked to immediately convince yourself that the definitions are equivalent, whereas in other cases, you may be asked to ponder about why the definitions are equivalent.
- There may be content in the guided tour page not directly related to the WHAT YOU NEED TO DO part. Typically, this additional content is separated from the main content by a separating box, saying WHAT's MORE. This is content you can go through, that might enhance your understanding of the content, but is not necessary to fully comprehend at this stage.
- If you want to check out some of the links in the guided tour page, make sure you open the links in a new tab/window so that you do not lose your position in the guided tour.
- Make a quick note of any doubts or thoughts that you have on reading a particular page. Some of these may be addressed later in the tour.
- At the end of each part, go through the factsheets, problem sets and confidence aggregators.
The guided tour is so designed that important concepts are continually repeated in different guises, at regular intervals. For instance, the definition of group is important, so apart from giving this definition at the outset, we continually return to examine this definition from different angles throughout the tour. Every time we return to a concept, we do so with a better picture of what is going on.
For readers following another reference
If you're following a standard textbook reference (either because you like it or because it is a course requirement) you may want to synchronize your learning experience at Groupprops, with the textbook. We are working on developing tools for this, which include:
- At the beginning of each part of the guided tour, we mention what the related chapters/sections in the textbook are
- At the end of each part of the guided tour, we mention where problems/exercises/riders related to that content, can be found in the textbook
Revisiting the guided tour
If you've already gone through the guided tour once, feel free to jump around in it when revisiting. If you've seen more stuff before, you might also find it useful to concentrate on the PONDER and WHAT'S MORE boxes in the page.
How the guided tour differs from the wiki at large
Thus, guided tour pages are so tailored that people can gradually build their knowledge in a subject, and the guided tour page on a topic is a relevant and small subset of the overall wiki page. From the guided tour page, you can go to the overall wiki page by clicking a link at the top saying This article adapts material from.
The guided tour is intended primarily for sequential use, so there is an order in which pages are meant to be read; on the other hand, there is no natural order or sequence to peruse content on the wiki. The wiki uses a number of organizational paradigms to aid navigation.
For beginners, useful page listings on the wiki at large include:
- Category:Basic facts in group theory
- Category:Results with direct proofs
- Category:Elementary non-basic facts in group theory