There are several major algorithms and mathematical techniques that are commonly used to solve industry problems across different domains. Here are some of the key ones:

1. Linear Regression: A statistical technique used to model and analyze the relationship between a dependent variable and one or more independent variables. It is widely used for predictive modeling and forecasting.
2. Logistic Regression: A statistical algorithm used for binary classification problems. It models the relationship between the dependent variable and independent variables to predict the probability of an event occurring.
3. Decision Trees: A machine learning algorithm that uses a tree-like model of decisions and their possible consequences. Decision trees are used for classification and regression tasks, providing interpretable rules for decision-making.
4. Random Forest: An ensemble learning method that combines multiple decision trees to improve prediction accuracy and reduce overfitting. It is commonly used for classification and regression tasks, as well as feature importance analysis.
5. Support Vector Machines (SVM): A machine learning algorithm used for both classification and regression tasks. SVM finds an optimal hyperplane to separate data points and maximize the margin between classes.
6. Neural Networks: Deep learning algorithms that mimic the structure and functioning of the human brain. Neural networks are used for tasks such as image and speech recognition, natural language processing, and time series analysis.
7. Clustering Algorithms: Techniques such as k-means, hierarchical clustering, and DBSCAN are used to group similar data points together based on their characteristics. Clustering is often applied in customer segmentation, anomaly detection, and pattern recognition.
8. Association Rules: Algorithms like Apriori and FP-Growth are used to discover relationships and patterns in large datasets. They are commonly used in market basket analysis and recommendation systems.
9. Time Series Analysis: Techniques such as ARIMA (AutoRegressive Integrated Moving Average) and exponential smoothing models are used to analyze and forecast time-dependent data, such as stock prices, sales trends, or energy demand.
10. Optimization Algorithms: Mathematical optimization techniques, including linear programming, integer programming, and evolutionary algorithms (e.g., genetic algorithms), are used to optimize resource allocation, production planning, scheduling, and other operational decisions.
11. Collaborative Filtering: A technique used in recommender systems to make predictions or recommendations by leveraging user behavior and preferences. It includes methods like user-based and item-based collaborative filtering.
12. Natural Language Processing (NLP): A field of AI focused on enabling computers to understand and process human language. Techniques such as text classification, sentiment analysis, named entity recognition, and machine translation are used for various applications.

These are just a few examples of the algorithms and mathematical techniques used in various industries. The choice of algorithm depends on the specific problem, the nature of the data, and the desired outcome. Often, a combination of different algorithms and techniques is employed to address complex industry challenges.