1. Engineering and scientific computing: Advanced mathematics plays an important role in engineering and scientific computing. For example, it can be used to solve complex physical problems, such as electromagnetic field, fluid mechanics, quantum mechanics and so on. In addition, it can also be used to optimize the design, simulate and predict the behavior of the system.
2. Economy and finance: Advanced mathematics is also widely used in the field of economy and finance. For example, it can be used to build economic models, analyze market behaviors and predict future trends. In addition, it can also be used for risk management, portfolio optimization and option pricing.
3. Computer science: Advanced mathematics also plays an important role in computer science. For example, it can be used in image processing, pattern recognition and machine learning. In addition, it can also be used in data compression, signal processing and cryptography.
4. Biology and medicine: Advanced mathematics is also widely used in biology and medicine. For example, it can be used to build biological models and analyze gene expression and protein structure. In addition, it can also be used in drug design and clinical trials.