1. Modeling: In engineering, we need to abstract and model real-world problems. Mathematics provides a powerful tool for us to create these models and use them to predict and solve problems.
2. Algorithm design: In the field of computer science and electronic engineering, we need to design and implement complex algorithms to solve specific problems. Mathematics provides a language that enables us to describe and understand these algorithms.
3. Data analysis: In engineering, we often need to deal with a lot of data. Mathematics provides a method that enables us to collect, analyze and interpret these data effectively.
4. Optimization: In many engineering problems, we need to find the optimal solution. Mathematics provides a theoretical framework that enables us to define and find these optimal solutions.
5. Theoretical proof: In engineering, we need to ensure that our design and solutions are correct. Mathematics provides us with methods to prove the correctness of these solutions.
Therefore, mathematics plays a vital role in designing new products and solving practical engineering problems. Without mathematics, we can't understand and solve these complicated problems. This is why we say that mathematics is the foundation of all engineering disciplines.