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MathSciNet search tips:

names:

The wildcard (*) may be used anywhere -however, if it is used at the beginning, it is ignored. TeX-coded accents are not required. For example, when searching for a name coded as m/"uller, you may use use m/"uller or muller, see example below:

Examples:
Erdos, P* will get authors with that exact last name and whose first name or initials start with the letter P (like Paul, Pavel, Peter, Petr, Pauline, etc.)
Knuth, Donald E. will get only authors with this exact name
Kap*sky, I* will get Kapinsky, Kaponsky, Kapowitsky, etc., whose first names or initials start with the letter I (Ivan, Illiya, Igor, Illich, etc.).
smith will get everything written by authors named Smith
Müller, m/uller, and muller will get the same results

Cyrillic
Effective January 1983, a new system for transliteration (romanization) of Cyrillic was adopted. This may affect author name searches (both last names and initials). In some cases, it may be necessary to do two searches, using first the current and then the old transliteration, in order to find all of the papers by a particular author. See the transliteration table for more information.

searching:

MathSciNet searches are not case-sensitive. A search for TopoLogy will get the same results as topology.

As with names, you can use an asterisk (*) to find variations in spelling and form (except MR Number and Mathematics Subject Classifications fields - MSC Primary/Secondary and MSC Primary). ALL searches will look for both the plural (or singular) of the words entered.

Searches AUTOMATICALLY look for both the singular and plural forms of a work. You can stop it from doing this by puttin an exclamation mark (!) at the end of a word. So, a search for "matrix" will match both "matrix" and "matrices" while "matrix!" will match "matrix" but not "matrices".

Boolean operators (AND, OR, NOT) may be entered between criteria.
To use a Boolean operator in a text input box, place the operator between the criteria. For example, in the Author field, type Graham AND Luckock to yield a headline list of papers co-authored by Graham and Luckock.

Alternatively, to achieve the same results, set two Field Name boxes to Author and set the Boolean operator between them to AND. Enter Graham in one input box and Luckock in the other input box.

If searching for a phrase that contains a Boolean operator, you must place the phrase in quotation marks, for example, "not locally symmetric".

Proximity Operators
This can be useful when searching for related expressions (a "family" of expressions that are variants of each other), while limiting the total number of words the expressions can contain. This is useful with searches that contain prepositions such as but, of and a. Since using such common words increases the chance of a time-out error. When searching for items that contain these words, consider using the proximity operators ADJ1, ADJ2, ADJ3, etc.

The database assumes adjacency, for example Vector ADJ1 Bundle is the same as a search of to Vector Bundle. The value of N in ADJN specifies one more than the maximum number of intervening words allowed between the two words connected by ADJN.

Examples:

1. ADJ2 allows one word or no words between the two words connected by ADJ2.

module adj2 differential
instead of
module of differential

as a criterion with Review Text set as the Search Field will return items containing "modules, differential", "module of differential", and "modules and differential",

2. ADJ3 allows up to two words between the two words connected by ADJ3

boolean function ADJ3 variables
instead of
boolean function of n variables

as a criterion with Review Text set as the Search Field will return items containing "boolean functions of $n$ variables", as well as items containing "Boolean function on two variables", "Boolean function over $k$ variables", "Boolean functions on $n$ variables", and " Boolean functions of many variables".

Search Criteria Containing Mathematics (TeX)
In the past, users needed to strip the TeX code from search terms in MathSciNet. This is no longer the case: For instance, a search on ${rm O}(3)$ will return results for, among others, Matrix elements of real representations of the groups ${rm O}(3)$ and ${rm SO}(3)$. Search terms are highlighted in the full item.

more tips are available at:

http://0-ams.rice.edu.janus.uoregon.edu/msnhtml/full_search_help.html
and
http://0-ams.rice.edu.janus.uoregon.edu/msnhtml/field_help.html