1) Research statements.

Search Google for "research statement" and an area of mathematics that you are interested in.

Here's a short selection:

http://people.uwec.edu/mbirika/Aba_Mbirika_Research_Statement.pdf

http://www-personal.umich.edu/~satriano/research.pdf

http://www.math.uconn.edu/~Ji%20LI/Research-statement-JiLi.pdf



2) Online availability of prefaces, contents, supplementary material, and sometimes draft versions for new books.

Use Google advanced book search to Search for all books published in the last year (or further back as you wish) and scroll through the listings until you find something that looks new to you. Once you find a promising looking book, after trying Google preview, go directly to the publisher's page for the book and also try to find the author's home page to look for additional material.

Example: At http://books.google.com/advanced_book_search enter "mathematics" in the subject box and enter "topology" in the "Find results" box. Publication date 2014-2014. 

On the second page of results the book "Topological Signal Processing" looks new.

Publisher's page: http://www.springer.com/engineering/signals/book/978-3-642-36103-6

Author's page: http://www.drmichaelrobinson.net/research.html