The career paths for mathematics and applied mathematics majors are very broad and cover many different fields. Here are some of the main career paths:

1. Education industry: many graduates of mathematics and applied mathematics majors choose to become teachers or professors, teaching mathematics courses at schools, universities, or research institutions.

2. Finance industry: Knowledge of mathematics and statistics is very important in the finance industry, so many graduates of mathematics and applied mathematics majors work in banks, insurance companies, investment companies and other financial institutions, such as risk managers, actuaries and quantitative analysts.

3. Data analysis: with the advent of the big data era, the demand for data analysts is growing. Graduates in Mathematics and Applied Mathematics can use their statistical and programming skills to analyze data in a variety of industries (e.g. retail, healthcare, telecommunications, etc.).

4. Software development: Many graduates in mathematics and applied mathematics also choose to enter the software development industry, using their logical thinking and programming skills to develop a variety of software products.

5. Research: Many graduates of mathematics and applied mathematics programs choose to continue their education and conduct research in mathematics or related fields.

6. Consulting: Knowledge of math and statistics can also be applied to the consulting industry, helping companies solve a variety of complex problems.

7. Technical Writing: Graduates in mathematics and applied mathematics can also use their expertise to write user manuals or technical documentation for technological products.

Overall, graduates of mathematics and applied mathematics programs can find work in many different industries, depending largely on their interests and career goals.