Mathematics

This page includes guidelines for two common citation styles, AMS and APA. If you are using another style and have questions, feel free to email the Science Librarian, Tessa Withorn (tessa.withorn@louisville.edu). 

Ask your professor which style they would like you to use for your assignment. If you get to choose, I highly recommend APA! 

• AMS
  • In-text
  • References
• APA
  • In-text citations
  • References

This guide is a quick introduction to the American Mathematical Society (AMS) citation style for in-text citations and references. Be sure to consult chapter 10 of the AMS Style Guide for full details on citing sources in AMS Style.

The most common way to cite sources in-text is to list references sequentially in brackets. If a reference is repeated, use the original reference number. The reference list is ordered numerically. 

Properties of feral curves include area and curvature estimates, energy thresholds, compactness, and asymptotic properties [1].

Some professors or journals may ask you to format your references in-text with the author's last name and the year in brackets [Fish2023], or the first letter of the author's last name and an abbreviation of the year [F23].

List the complete citation at the end of the paper in a References or Bibliography section. Citations will vary depending on the type of source. 

Journal article

1. Author(s), Listed as first initial or name and last name. 

2. Title of the article, In italics and sentence case, meaning only the first word of the title or subtitle and any proper nouns are capitalized. 

3. Shortened Journal Title. Some journal abbreviations will be included with the article information, otherwise look up the abbreviation of names from MathSciNet. 

4. Volume Number In bold. 

5. (Year),

6. Issue number, List as no. #.

7. Page range,

8. DOI Include only the digital object identifier (DOI) string (not the https://) after DOI.

[1] Joel W. Fish, and Helmut Hofer, Feral curves and minimal sets, Ann. of Math. 179 (2023), no. 2, 533-738, DOI 10.4007/annals.2023.197.2.2

Book

1. Author(s), Listed as first initial or name and last name. 

2. Book title, In italics and sentence case, meaning only the first word of the title or subtitle and any proper nouns are capitalized. 

3. Volume number, If available. Listed as Vol., #. May also include the name of a series. 

4. Publisher, 

5. Publisher's city, 

6. Year. 

[2] Luiz Paulo Fávero, Patrícia Belfiore, and Rafael de Freitas Souza, Data science, analytics and machine learning with R, Academic Press, Cambridge, 2023. 

Website

1. Author(s), Listed as first initial or name and last name. If there is no listed author, list the publisher first instead. 

2. Publisher, Usually the name of the website. 

3. Title of webpage In sentence case, meaning only the first word of the title or subtitle and any proper nouns are capitalized. 

4. (Date), List as much detail as is available for publication date or date last updated. 

5. URL. 

[3] Allechar Serrano López, American Mathematical Society, The Jordan curve theorem as a lusona (2023), https://mathvoices.ams.org/featurecolumn/2023/02/01/the-jordan-curve-theorem-as-a-lusona/

This guide is a quick introduction to the American Psychological Association (APA) Style for in-text citations and references. Be sure to consult the Publication Manual of the APA or the APA Style website for detailed standards and procedures.

You can also find sample papers with annotations and a Word template on APA Style's website. 

When you reference another source, use an in-text citation in the body of your paper.

Paraphrasing or summarizing the main findings or takeaways from a research article is the preferred method of citing sources in an APA paper. Always include the last name of the author(s) and the year of the article, so your reader can find the full citation in the reference list. These citations can be written narratively or in parentheses at the end of the sentence. Any sentence punctuation goes after the closing parenthesis. See more examples of formatting parenthetical versus narrative in-text citations from APA Style's official website.

Narrative In-text Citation

According to Shavers (2007), limitations of studying socioeconomic status in research on health disparities include difficulties in collecting data on socioeconomic status and the complications of classifying women, children, and employment status.

Parenthetical In-text Citation

Limitations of studying socioeconomic status in research on health disparities include difficulties in collecting data on socioeconomic status and the complications of classifying women, children, and employment status (Shavers, 2007).

If you're quoting the exact words of someone else, include an in-text citation with the page number(s). See more examples of quotations from APA Style's website. 

In-text citations differ depending on the number of authors listed for a work, and if there is a group author.

1 Author

You only need the author's last name comma year in parentheses.

(Abrams, 2018)

2 Authors

Connect both authors' last names with & (ampersand) comma and the year.

(Wegener & Petty, 1994)

3 or More Authors

If there are 3 or more authors use et al., which is Latin for "and others," comma and the year.

(Harris et al., 2018)

Group Author

First time with an abbreviation:

(Centers for Disease Control and Prevention [CDC], 2019)

Then all subsequent citations:

(CDC, 2019)

Include the complete citation at the end of your paper in a references section. References are organized by the author's last name in alphabetical (A-Z) order. Use an hanging indent to separate each list item.

Use the following directions and examples to format these common types of sources. You can find a comprehensive list of reference examples on APA's website. 

Journal Article

1. Author(s). List each author's last name and initials as Author, A. A., Author, B. B., & Author, C. C. Use an ampersand (&) before the final author's name. Read more from the APA Style website if there are 21 or more authors.

2. (Year).

3. Title of the article. For works that are part of a greater whole (e.g. articles, chapter), use sentence case. Only the first word of the title and subtitle and proper nouns are capitalized.

4. Title of the Journal, Italicize and capitalize each word in the journal. You can use headline-style capitalization. 

5. Volume Italicize the journal volume number. If there is no issue, include a comma before the page range.

6. (Issue), If there is a issue number in addition to a volume number, include it in parentheses.

7. Page range. If there is no page range within the journal volume/issue, this can be excluded.

8. DOI (Digital Object Identifier) This is a direct link to the article on the publisher's website. Read more about DOIs from APA Style's website.

Toledo, D., Sanderson, M., Spaeth, K., Hendrickson, J., & Printz, J. (2014). Extent of Kentucky bluegrass and its effect on native plant species diversity and ecosystem services in the Northern Great Plains of the United States. Invasive Plant Science and Management, 7(4), 543-552. https://doi.org/10.1614/IPSM-D-14-00029.1

Book

1. Author(s). List each author's last name and initials as Author, A. A., Author, B. B., & Author, C. C. Use an ampersand (&) before the final author's name.

2. (Year).

3. Title of the book. Note: For works that stand alone (e.g. books, reports), italicize the title. Only capitalize the first word of the title and subtitle and any proper nouns.

4. (Edition). If there is an edition or volume, include it in parentheses and use abbreviations of ed. or vol.

5. Publisher. You do not need to include the publisher location or databases where you retrieved it.

Richtel, M. (2019). An elegant defense: The extraordinary new science of the immune system (1st ed.). William Morrow.

Book Chapter with Editors

1. Author(s). List each chapter author's last name and initials as Author, A. A., Author, B. B., & Author, C. C. Use an ampersand (&) before the final author's name.

2. (Year).

3. Title of the chapter. For works that are part of a greater whole (e.g. articles, chapter), use sentence case. Only the first word of the title and subtitle and proper nouns are capitalized.

4. In Editor(s), List each editor's initials and last name as A. A. Editor, B. B. Editor, & C. C. Editors, include (Ed.) or (Eds.) in parentheses, and end with a comma.

5. Title of the book For works that stand alone (e.g. books, reports), italicize the title. Only capitalize the first word of the title and subtitle and any proper nouns.

6. (pp. xx-xx).

7. Publisher. You do not need to include the publisher location or databases where you retrieved it.

Khan, J. S., Provencher, J. F., Forbes, M. R., Mallory, M. L., Lebarbenchon, C., & McCoy, K. D. (2019). Parasites of seabirds: A survey of effects and ecological implications. In C. Sheppard (Ed.), Advances in marine biology (pp. 1-50). Academic Press. 

Website

1. Author(s). List each author's last name and initials as Author, A. A., Author, B. B., & Author, C. C. If there is no author, spell out the name of the organization or site.

2. (Year, Month Date). Read more about date formats from the APA Style website. Provide as specific a date as is available. Use the date last updated, but not the date last reviewed or copyright date. If there is no date, use (n.d.).

3. Title of page or section. Italicize the title of the page and use sentence case.

4. Source. Usually the official name of the website. If the source would be the same as the author, you can omit the source to avoid repetition.

5. URL

Healing Mushrooms. (n.d.). A comprehensive list of common wild mushrooms in Kentucky. https://healing-mushrooms.net/kentucky